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{{Dormant}}
: ''Rename this page to '''WP:Manual of Style/Physics''' when complete and universally agreed on by [[Wikipedia:WikiProject Physics|wikiproject physics]].''

This part of Wikipedia's [[Wikipedia:Manual of Style|Manual of Style]] contains guidelines for consistency of style in writing and editing articles on [[physics]] as well as physics-related parts of other articles. For consistency with the rest of Wikipedia, other manuals of style (in particular [[WP:MOSMATH]] for mathematics and [[WP:MOSCHEM]] for chemistry) apply when possible. Exceptions and additional conventions specific to physics topics are described here.

== Typesetting of formulae ==
{{See also|WP:MOSMATH#Typesetting of mathematical formulae|Help:Displaying a formula|WP:«math»}}

=== LaTeX versus HTML ===
There are a number of different techniques to produce mathematical formulae on Wikipedia, all with their advantages and disadvantages. Inevitably, this has led to a wide spectrum of preferences among editors and of styles used in articles. Even worse, there is a perpetual change of formatting by editors who don't like the current style of an article.

The main technical options are:
* [[LaTeX]] (generated using [[Wikipedia:«math»|<nowiki><math></nowiki>]]),
* Wiki markup and [[HTML]], together with [[Unicode]] characters,
* the {{tl|math}} and {{tl|mvar}} templates.

The main principles to be considered when deciding about a particular formatting are ''consistency'' and ''consensus''. Don't set one formula in a style very different from the rest of the article, and don't do mass changes from one style to another without prior discussion on the talk page. That said, the style recommended for physics articles is as a rule of thumb:
* use wiki markup or the {{tl|math}} template for ''inline'' formulae,
* use <nowiki><math>...</math></nowiki> for ''displayed'' formulae.

This choice is aiming at a smooth integration of simple inline formulae in the surrounding text, while offering the extended possibilities of LaTeX formatting for more involved displayed formulae.<!-- explain what inline/displayed means -->

=== Roman versus italic ===
One of the most basic, though often ignored typesetting conventions for mathematical formulae concerns the use of upright ([[roman type|roman]]) versus [[italic type|italic]] typeface: as a general rule, 
* ''variables'' (including indices and physical quantities) should be set ''italic'', while 
* ''names'' (including abbreviations, names of particles, chemical elements and units of measurement) should be set in roman type. 

This rule explicitly applies also to [[#Subscripts and superscripts|subscripts and superscripts]]. Paying attention to this seemingly minor detail helps to immediately make clear the meaning of a particular notation, and should not be seen as [[Nitpicking (pastime)|nitpicking]]. The rule has a few notable exceptions, which will be explained below. <!-- add links. multi-letter vars and functions upright -->

=== Greek letters ===

The [[Greek alphabet]] is extensively used throughout physics and mathematics. Due to technical limitations, the <code>&lt;math>...&lt;/math></code> environment always typesets lower case Greek letters in italic, and upper case ones in roman type. For consistency within an article, Greek letters produced using HTML or {{tl|math}} should thus follow the same convention. This practice applies to both normal and bold font weight.

Lower case Greek letters that denote names of particles, and that don't appear in the same article within a <code>&lt;math></code> environment, should be set in roman type, following the [[#Roman versus italic|general style]] for names.

Some Greek letters have a second, ''variant'' form, for example {{User:Hhhippo/sxt|<math>\varepsilon</math>|title=<nowiki><math>\varepsilon</math></nowiki>}} vs. {{User:Hhhippo/sxt|<math>\epsilon</math>|title=<nowiki><math>\epsilon</math></nowiki>}}, {{User:Hhhippo/sxt|<math>\varphi</math>|title=<nowiki><math>\varphi</math></nowiki>}} vs. {{User:Hhhippo/sxt|<math>\phi</math>|title=<nowiki><math>\phi</math></nowiki>}}, or {{User:Hhhippo/sxt|<math>\vartheta</math>|title=<nowiki><math>\vartheta</math></nowiki>}} vs. {{User:Hhhippo/sxt|<math>\theta</math>|title=<nowiki><math>\theta</math></nowiki>}}. If they are used, the same symbol should be used for the same quantity consistently throughout the article. (There is also a variant for the lowercase <code>l</code> in the Latin alphabet, {{User:Hhhippo/sxt|<math>\ell</math>|title=<nowiki><math>\ell</math></nowiki>}}, which can be useful for the distinction from an upper case <code>I</code>.)

== Units and quantities ==

Quantities whose values are not given numerically, including both [[variable (mathematics)|variables]] and [[physical constant]]s, are denoted [[#Common mathematical formulae|in a way similar to variables in mathematics]]. Examples are
* the [[speed of light]], {{math|''c''}}&nbsp;=&nbsp;{{physconst|c|ref=no}};
* the [[reduced Planck constant]], {{math|''ħ''}}&nbsp;=&nbsp;{{physconst|hbar|ref=no}}
* the [[vacuum permittivity]], {{math|''ε''<sub>0</sub>}}&nbsp;=&nbsp;{{physconst|eps0|ref=no}}
* the [[elementary charge]], {{math|''e''}}&nbsp;=&nbsp;{{physconst|e|ref=no}};
* the [[electron rest mass]], {{math|''m''<sub>e</sub>}}&nbsp;=&nbsp;{{physconst|me|ref=no}}.

One must carefully distinguish ''[[physical quantity|quantities]]'', ''[[unit of measurement|units]]'', and ''[[dimensional analysis|dimensions]]'', because different typographies apply to them. For example:
* [[Voltage]]<!--ref>The [[voltage]] article needs fixing!</ref>  Needed by 2014, no more a problem.
--> is a quantity and may be denoted as {{mvar|V}}, an [[italic type|italic]] capital letter "[[V]]".
* The [[volt]] is a unit and must be denoted as V, a roman capital letter.  Brackets [] mean ''the units of'', so [''V''] = V, and braces {} mean ''the numerical value of'' so ''V'' = {''V''}[''V''].
* The dimension of voltage should be written in terms of the base dimensions in [[roman type|roman]] sans-serif type:<ref>JCGM, ''International vocabulary of metrology – Basic and general concepts and associated terms (VIM)''</ref> ML<sup>2</sup>T<sup>−3</sup>I<sup>−1</sup>.

When a physical constant serves as a unit in some systems, such as in with [[atomic units]], it should be denoted as a constant (in italics).  In particular, the elementary charge, even when treated as a unit, is denoted {{math|''e''}}, notwithstanding that it was originally a unit (named the electron, with symbol {{math|e}}) (see ''{{section link|Elementary charge|As a unit}}'').  These symbols are also never prefixed with SI prefixes. Related units that are denoted in roman type include
* the [[unified atomic mass unit]], symbol {{math|u}};
* the [[Dalton (unit)|dalton]], symbol {{math|Da}};
* the [[electronvolt]], symbol {{math|eV}}.

Generally, all symbols (abbreviations) of units are universally [[Roman type|roman]] (upright). For dimensions, an exception occurs when denoting the dimension of an arbitrary quantity is necessary, as in "[quantity]"; see [[continuity equation#Preliminary description|continuity equation]] for an example of this case. <!-- for a convenient diff; remove later.--> 
Representation of units and numerical quantities (where a numerical value and a unit are specified explicitly) should comply with ''{{section link|WP:Manual of Style/Dates and numbers#Scientific notation, engineering notation, and uncertainty}}'' unless the present Manual specifies otherwise. See also: {{tl|val}}.

The [[#Roman versus italic|roman versus italic]] guideline applies to units. For example, write 
: {{xt|1=''P'' = ''P''<sub>0</sub> + 9807 Pa/m × ''h''}},
but not
: {{!xt|1=''P'' = ''P''<sub>0</sub> + 9807 ''Pa''/''m'' × ''h''}}.

== Common mathematical formulae ==

Examples:
* [[Newton's second law]]:
*: <math>\mathbf{F} = \frac{d\mathbf{p}}{dt}</math> 
* [[Schrödinger equation]]: displayed (see [[#angle brackets|below]] for angular brackets),
*: <math>i\hbar\frac{d }{d t}\left|\Psi\right\rangle = \hat{H}\left|\Psi\right\rangle\,.</math>

Representation of Common mathematical formulae (arithmetic, algebra (including [[vector space|vectors]] and [[tensor]]s), [[summation]], [[Integral|integration]], [[Derivative|differentiation]], [[differential geometry]], [[complex analysis]] ...) should comply with ''{{section link|WP:Manual of Style/Mathematics #Typesetting of mathematical formulae}}'' unless the present Manual specifies otherwise. Notations that are popular in a certain context should be used; unusual or otherwise less common notation (for physics) should be avoided.

=== Functions ===

Exponential functions are very common in physics, representing growth and decay from solutions of [[differential equation]]s, [[complex number]] representations, and [[group theory|group]] [[generator (mathematics)|generator]]s. As such they can have quite large/complicated variables. 
* For simple arguments on one line, the ''e'' notation is legitimate 
*: <math>e^{i 2\pi x/\lambda}, e^{i \omega t} </math>
: in which case fractions should use the ''forward slash /'', not <code>\frac{}{}</code>.
* For more detailed/complicated arguments, (see [[angular momentum#Total angular momentum as generator of rotations|angular momentum]] and [[Schrödinger equation#Solution to equation|Schrödinger equation]] respectively), the "exp" notation is clearer to read:
:: {{xt|<math>R(\hat{n},\phi) \equiv \exp\left(-\frac{i}{\hbar}\phi\, \mathbf{J}\cdot \hat{\mathbf{n}}\right)\,,\quad \exp\left[i(\mathbf{p}\cdot\mathbf{x}-Et)/\hbar\right]</math> }}
: however using the forward slash for division as above is acceptable, although extra brackets are usually needed,
:: {{!xt|<math>R(\hat{n},\phi) \equiv e^{  - i\phi\, \mathbf{J}\cdot \hat{\mathbf{n}} /\hbar}\,,\quad e^{i(\mathbf{p}\cdot\mathbf{x}-Et)/\hbar}</math>}}
: whereas fractions using the horizontal stroke are not:
:: {{!xt|<math>R(\hat{n},\phi) \equiv e^{-\frac{i}{\hbar}\phi\, \mathbf{J}\cdot \hat{\mathbf{n}}}\,,\quad e^{\frac{i}{\hbar}(\mathbf{p}\cdot\mathbf{x}-Et)}</math>}}

=== Vectors and vector spaces ===
<!---PLEASE LEAVE THE BOLD/OVERARROWED/UNDERARROWED/BOLD-ITALIC TEXT ALONE, TO SHOW WHAT IT LOOKS LIKE--->
* For [[Euclidean vector]]s, there are numerous conventions. The better notations for vectors use:
** '''bold''': easy to typeset and print, and stands out, easily compatible with other [[diacritic]]s, or 
** <math>\overrightarrow{\text{overarrows}}</math> or <math>\underline{\text{underlining}}</math>: easy to hand-write and indicates clearly a quantity with direction, although it becomes messy with other [[diacritic]]s. Underlining is easily possible in HTML using the <code><nowiki><u> </u></nowiki></code> tags, like this: ''<u>A</u>'', ''<u>x</u>''. There is the template {{tl|vec}} for HTML left/right/doubleheaded arrows over/under one letter, like this: {{vec|''a''}}, {{vec|''Z''|double|under}} etc.
** <math>\overline{\text{overlining}}</math>: is often used for position vectors for example the position vector from point A to B would be written <math>\overline{\text{AB}}</math>: 
** In practice, '''''bold italic''''' is also employed, but is less common than upright. For consistency throughout articles, please use upright bold. In particular, please do not execute mass changes from bold style to bold-italic.
**: {{xt|{{math|'''A'''}}, <math>\mathbf{A}</math>}}, not {{!xt|{{math|'''''A'''''}}, <math>\boldsymbol{A}</math>,  <math>\overrightarrow{A}, \overrightarrow{AB} </math>}}
* For "normal" or [[unit vector]]s, they can be bold, or a hat ''replaces'' the arrows:
*: {{xt|{{math|'''ê'''}}, <math>\mathbf{\hat{e}}, \hat{e}</math> }}, not {{!xt|<math>\overrightarrow{\hat{e}}</math>}}
* {{anchor|angle brackets}}[[Quantum state]] vectors, which are elements of a [[Hilbert space]], should use the [[bra-ket notation]], the standard in [[quantum mechanics]], rather than bold, arrows, or hats. For the bra-ket notation, the {{tl|langle}} and {{tl|rangle}} templates may be used to generate HTML/Unicode equivalents for the \langle and \rangle glyphs of <nowiki><math></nowiki> mode. There are also specialized templates {{tl|bra}} {{tl|ket}} for creating bra and ket vectors, and {{tl|bra-ket}} for inner products.
*: {{xt|{{ket|''ψ''}}, {{bra|''ψ''}}, {{math|{{ket|''ψ''}}}}, {{math|{{bra|''ψ''}}}}, <math>\left|\psi\right\rangle, \left\langle\psi\right|</math> }}, not {{!xt|<math>\overrightarrow{\psi},\boldsymbol{\psi},\hat{\psi}</math>}}
* [[operator (physics)|Operators]] usually have a hat, but not always ({{math|''Â''}} vs. {{math|''A''}}). Either is acceptable as long as the meaning is unambiguous. For example, when describing an [[eigenvalue]] of an operator using the same letter as for the operator itself, the operator should have a hat to distinguish the two.
* For tensors ''not in index notation'', use one of sans serif, bold sans serif, bold italic '''''T''''' ... (to be decided). Do not use [[blackboard bold|𝕓𝕝𝕒𝕔𝕜𝕓𝕠𝕒𝕣𝕕 𝕓𝕠𝕝𝕕]], which are reserved for sets (see below [[#sets and spaces|sets and spaces]]).
*: {{xt|{{math|'''''A'''''}}, <math>\boldsymbol{A}, \, \mathsf{A}, \, \boldsymbol{\mathsf{A}}</math> }}, not {{!xt|<math> \mathbb{A}</math>, {{math|𝔸}} }}
* For [[tensor contraction|contraction]] in a Hilbert space, one should use [[bra-ket notation]], not the [[sesquilinear form#Hermitian form|Hermitian form]] notation:
*: {{xt|<math>\langle\phi | \psi \rangle</math> |title=<nowiki>LaTeX: <math>\langle\phi | \psi \rangle</math> HTML: {{bra-ket|''ϕ''|''ψ''}}   or   {{math| {{bra-ket|''ϕ''| ''ψ''}} }}</nowiki> }}, not {{!xt|<math>\langle \phi, \psi \rangle</math> }}.
* The use of [[dot product]] and [[del]] operators for Minkowski space may lead to confusion, especially so in indefinite-metric spaces even between {{math|(1, 0)}}- and {{math|(0, 1)}}-tensors. Also, if the article has to operate with both vectors and higher [[tensor]]s, then the use of different styles for tensor fields of different types would be confusing too, even in [[3-dimensional space]]:
*: {{xt| {{math|''v''<sup>''μ''</sup>∂<sub>''μ''</sub>''f'' }} |title=<nowiki>{{math|''v''<sup>''μ''</sup>∂<sub>''μ''</sub>''f''  }}</nowiki>}} or {{xt| {{math|''v''<sup>''μ''</sup>∇<sub>''μ''</sub>''f'' }} |title=<nowiki>{{math|''v''<sup>''μ''</sup>∇<sub>''μ''</sub>''f'' }} </nowiki>}}, not {{!xt| {{math|(∇''f'' )· '''v'''}}}}.

=== Subscripts and superscripts ===

Subscripts and superscripts follow the general rule about [[#Roman versus italic|roman versus italic]] typeface. For example:
: {{User:Hhhippo/sxt|{{math|'''F'''<sub>ext</sub>}}|title=<nowiki>{{math|'''F'''<sub>ext</sub>}}</nowiki>}},&nbsp;&nbsp; {{User:Hhhippo/sxt|<math>2\rho_{\mathrm{Al}} < \rho_{\mathrm{Fe}}</math>|title=<nowiki><math>2\rho_{\mathrm{Al}} < \rho_{\mathrm{Fe}}</math></nowiki>}},&nbsp;&nbsp;{{User:Hhhippo/sxt|<math>\mathbf{B}_{x_0}^\mathrm{ext}(t)</math>|title=<nowiki><math>\mathbf{B}_{x_0}^\mathrm{ext}(t)</math></nowiki>}},
rather than
: {{User:Hhhippo/!sxt|{{math|'''F'''<sub>''ext''</sub>}}|title=<nowiki>{{math|'''F'''<sub>''ext''</sub>}}</nowiki>}},&nbsp;&nbsp; {{User:Hhhippo/!sxt|<math>2\rho_{Al} < \rho_{Fe}</math>|title=<nowiki><math>2\rho_{Al} < \rho_{Fe}</math></nowiki>}},&nbsp;&nbsp; {{User:Hhhippo/!sxt|<math>\mathbf{B}_\mathrm{x_0}^\mathrm{ext}(t)</math>|title=<nowiki><math>\mathbf{B}_\mathrm{x_0}^\mathrm{ext}(t)</math></nowiki>}}.

Note that in the last example, "ext" is a text label (an abbreviation for "external") and is thus set roman, while ''x''<sub>0</sub> is a variable and is this set in italic. This type of notation is sometimes used instead of {{nowrap|'''B'''<sup>ext</sup>(''x''<sub>0</sub>, ''t'')}} to indicate that only the functional dependence of '''B''' on ''t'' is of interest, while ''x''<sub>0</sub> is a parameter held fixed (though conceptually still a variable).

An exception can be made when the [[Help:Displaying a formula|&lt;math> tag]] has to be used, and an intended glyph is not available in [[WP:«math»#Comparison of presentations|its renderers]], such as non-italicized Greek letters. For example, when typesetting the mass of a [[neutrino]] ν (nu) in html or {{tl|math}}, the ν can remain non-italic:
: {{math|''m''<sub>ν</sub>}}, 
while in &lt;math>;
: <math>m_{\mathrm\nu}</math> (with <code>\mathrm</code> applied to <code>\nu</code>)
looks no different than 
: <math>m_\nu</math> (without the <code>\mathrm</code>) 
and the latter may be used.

==== Index notation for tensors and spinors ====

Two ways to denote [[Vector (mathematics and physics)|vector]]s, [[tensor]]s, and [[spinor]]s (also [[vector field]]s, [[tensor field]]s, and [[spinor field]]s) are:
# as the full entity with no reference to specific components (which uses the boldface notations above), or
# in components via [[index notation]] (cf. ''[[Ricci calculus]]'' and ''[[Van der Waerden notation]]''), with or without reference to a [[Basis (linear algebra)|basis]].

Generally, the first is used in simpler contexts, while index notation is used to make advanced manipulations simpler. The [[linear operator]] notation is depreciated (with possible exception of [[theoretical mechanics]] and other domains where index notation is traditionally avoided).{{clarification needed}}

* Letters that ''are'' [[index notation|indices]] for [[tensor]]s or [[spinor]]s (see for example [[Ricci calculus]] and [[Van der Waerden notation]]) should be italicized. A specific script used as a tensor index may give a hint about nature of the corresponding linear space&nbsp;– this distinction should be used whenever possible. For example, [[spacetime]]-based (four dimensional) objects should be indexed with a subset of lowercase [[Greek alphabet|Greek]] letters:
*: {{math|''A''<sup>''μ''</sup>}} or <math>A^\mu.</math>
: Ideally - not all Greek letters are used for indices. For example, ''ϕ'' and ''ψ'' are excluded due to its heavy usage as wave functions and fields, and ''η'' is used to denote the [[Minkowski space|standard (Minkowskian) metric]].
* Objects constructed of weight-{{frac|1|2}} [[spin representation]]s of the [[Lorentz group]] should be indexed with capital Latin letters:<ref>See, for example, {{Citation |no-tracking=yes| last1=Penrose | first1=Roger | author1-link=Roger Penrose | title=The twistor programme | doi=10.1016/0034-4877(77)90047-7 | mr=0465032 | year=1977 | journal=Reports on Mathematical Physics   | volume=12 | issue=1 | pages=65–76|bibcode = 1977RpMP...12...65P }}</ref>
*: {{math|φ<sub>''A''</sub>}} or <math>\varphi_A.</math>
*Most of other linear spaces, including [[3-dimensional space]], use lowercase [[Latin alphabet|Latin]] letters: 
*: {{math|''A''<sup>''i''</sup>}} or <math>A_i,.</math>
:(although the letters&nbsp;{{mvar|i, j}} may cause confusion where [[complex numbers]] are used; this should be clarified in the context),
:: {{math|''A''<sup>''k''</sup>}} or <math>A^k.</math> 
: Note that {{tl|ell}} is equivalent to [[ℓ]]. Distinction of indices is especially helpful when one tensor quantity is built on [[tensor product|several linear spaces]] of different natures.

=== Calculus ===

* If "d" is used in [[differential of a function|differential]]s or [[derivative]]s, it should be ''italic'' or upright throughout; mixed styles look irregular.
* In vector expressions for the gradient ∇, with respect to a given basis, the basis vectors should be ''in front'' of the derivative operators. In [[three-dimensional|3d]] [[Cartesian coordinates]]:
*: {{xt|{{math|∇ {{=}} '''ê'''<sub>''x''</sub>{{sfrac|∂|∂''x''}} + '''ê'''<sub>''y''</sub>{{sfrac|∂|∂''y''}} + '''ê'''<sub>''z''</sub>{{sfrac|∂|∂''z''}}}} or <math>\nabla = \hat{\mathbf{e}}_x \frac{\partial}{\partial x} + \hat{\mathbf{e}}_y \frac{\partial}{\partial y} + \hat{\mathbf{e}}_z\frac{\partial}{\partial z} </math> }}
: and not
:: {{!xt|{{math|∇ {{=}} {{sfrac|∂|∂''x''}} '''ê'''<sub>''x''</sub>+ {{sfrac|∂|∂''y''}}'''ê'''<sub>''y''</sub> + {{sfrac|∂|∂''z''}}'''ê'''<sub>''z''</sub>}} or <math>\nabla = \frac{\partial}{\partial x} \hat{\mathbf{e}}_x + \frac{\partial}{\partial y} \hat{\mathbf{e}}_y + \frac{\partial}{\partial z} \hat{\mathbf{e}}_z</math>}}
: and similarly for any other coordinates. It is clear this way that the derivatives are operators not acting on the basis vectors (which can have spatial dependence in a local coordinate frame).
* When using <nowiki><math></nowiki>, use either <math>\nabla</math> (<code>\nabla</code>) or <math>\bigtriangledown </math> (<code>\bigtriangledown </code>) throughout - it looks irregular to mix the styles.
* The capital delta symbol is universally reserved for changes in quantities, for example Δ''x'' for change in position coordinate ''x''.
* The same symbol Δ is also used in mathematics <!--- how often in physics?--->to denote the [[Laplacian operator]]. Where possible, please use the "nabla squared" symbol ∇<sup>2</sup>, which appears to be more common in physics, and is more intuitive; ∇<sup>2</sup> = ∇ ⋅ ∇ is a nicer notation, and less ambiguous for capital delta.
* The symbol {{math|''&part;<sub>α</sub>''}} is used for the [[four gradient]] operator (indexed components), as usual. There are other notations, including <!---maybe rare, although I have seen them used before--->
** <math>\Box</math>, which should be reserved for the [[D'Alembertian operator]] (see next point). 
** {{math|''D''}}, which should be reserved for some [[covariant derivative]] (see next point).
* The symbol <math>\Box</math> is used for the [[D'Alembertian operator]]. There are other notations, including 
** <math>\Box^2</math>, to parallel the Laplacian ∇<sup>2</sup>. The notation without the square is already known to denote the D'Alembertian. Either can be used (?)
** {{math|''D''}} or {{math|''D''<sup>2</sup>}} (very rare<!---but I have seen it used before--->), which should be reserved for some [[covariant derivative]] (?) 
: {| class=wikitable style="margin-left:2em" valign=center
 !Setting
 ! bgcolor=#FF9999 |Not recommended
 !Recommended
 |-
 |[[Laplacian operator]]
 | bgcolor=#FF9999 |{{math|Δ}}
 |{{math|∇<sup>2</sup>}}
 |-
 |[[Four gradient]]
 | bgcolor=#FF9999 |{{math|''D''}}, <math>\Box</math> etc.
 |{{math|&part;<sub>α</sub>}}
 |-
 |[[D'Alembertian operator]]
 | bgcolor=#FF9999 |{{math|''D'', ''D''<sup>2</sup>}} <math>\Box^2</math> etc.
 |<math>\Box, \partial_\alpha\partial^\alpha</math>
 |-
|}
* For integrals, either of the notations are employed in the literature:
*: {{math|<big>&int;</big> ''f''(''x'') ''dx'', <big>&int;</big> ''dx'' ''f''(''x'')}} or <math>\int f(x)\,dx, \,  \int\,dx f(x)</math>
: and either is acceptable in WP physics articles. 
* For {{tl|math}}, [[integral symbol]]s can be produced using the same syntax as for LaTeX using the {{tl|intmath}} template. 
* For integrations over the [[Boundary (topology)|boundary]] of a (hyper)volume ''V'', the partial symbol {{math|∂}} denoting the boundary of a closed volume is encouraged ('''including''' a brief explanation such as "where {{math|∂''V''}} is the boundary of the volume ''V''"); it is a powerful and compact notation:
*: {{math|<big>&int;</big> <sub>∂''V''</sub> ψ('''x''') ''dV''}} or <math>\int_{\partial V} \psi(\mathbf{x})\,dV</math>
: and removes the need to use ''another symbol'' for the boundary of the volume.
* There is an [[abuse of notation]] where integrands are ''not enclosed in brackets'', frequently the case when (say) [[Green's theorem]] in a 2d plane is applied:
*:{{!xt|{{math|<big>∮</big> <sub>∂''D''</sub> ''p''(''x'', ''y'') ''dx'' + ''q''(''x'', ''y'') ''dy''}} or <math>\oint_{\partial D} p(x,y)\,dx + q(x,y)\,dy</math>}},
: which really means:
:: {{xt|{{math|<big>∮</big> <sub>∂''D''</sub> [ ''p''(''x'', ''y'') ''dx'' + ''q''(''x'', ''y'') ''dy'' ]}} or <math>\oint_{\partial D} \left[ p(x,y)\,dx + q(x,y)\,dy\right]</math> }}
: The brackets are often dropped by sources since it is known the integral symbol always includes the differentials (in the above example "{{math|''dx''}}" and "{{math|''dy''}}"). Nevertheless: for the sake of clarity an extra pair of brackets will not clutter, and should be included.

==== Ratios of differential (infinitesimal) quantities and derivatives ====

{{see also|Notation for differentiation}}
In physics, ratios of [[differential (infinitesimal)]] quantities frequently occur, and share the same notation with first order [[derivative]]s, which also frequently occur. For example, the local [[charge density]] of an electrically charged continuum is given by the ''ratio'' of the infinitesimal charge {{math|''dq''}} in infinitesimal volume {{math|''dV''}}:
: <math>\rho =\dfrac{dq}{dV} </math>

However, this looks like a ''derivative'' of {{math|''q''}} with respect to {{math|''V''}}. In cases like this, notations can be misleading, as
* the derivative is defined as a [[Limit (mathematics)|limit]]ing [[difference quotient]], but also an [[Operator (mathematics)|operator]] (cf. [[linear algebra]]),
* calculating the [[differential of a function]] is a general way to determine infinitesimal changes of a quantity using a derivative.

So these are not exactly the same, differentials are more general. Following are the recommended applications of the notation.

: {| class="wikitable"
|-
! Operations 
! Notation
! Usage in the literature
|-
| Division of infinitesimal quantities {{math|''dy''}} and {{math|''dx''}}
| {{math|{{sfrac|''dy''|''dx''}}, {{frac|''dy''|''dx''}}, ''dy''/''dx''}}
| Ratios ''or'' derivatives
|-
| Derivative of {{math|''y'' {{=}} ''y''(''x'')}} as a [[function (mathematics)|function]] of {{math|''x''}}
| {{math|{{sfrac|''d''|''dx''}}''y''}}
| Used only for derivatives, not ratios as above. Advantages include:
* makes clear that differentiation is an operator,
* clarifies notation for higher derivatives by repeated action of a derivative,
*: {{math|{{sfrac|''d<sup>n</sup>''|''dx<sup>n</sup>''}}''y'' {{=}} {{sfrac|''d''|''dx''}}...{{sfrac|''d''|''dx''}}{{sfrac|''d''|''dx''}}''y''}}
|-
|}

For partial derivatives this is not a problem, since differentials are never written as "{{math|''∂x''}}"; only the full symbol of a partial derivative, in any of the equivalent notations;
: {{math|{{sfrac|''∂F''|''∂x''}}, {{sfrac|''∂''|''∂x''}}''F'', {{frac|''∂F''|''∂x''}}, {{frac|''∂''|''∂x''}}''F'', ''∂F''/''∂x'', }}
has meaning.

== Particles, substances and reactions ==

*Symbols for subatomic particles and nuclei can be generated with {{tl|Subatomic particle}} and [[:Category:Nuclide templates|Nuclide templates]], otherwise they should be typographically similar. 
*Where chemical notation is used, it should comply with [[WP:MOSCHEM]]. 
*Formulae of (nuclear or particle) reactions should not be formatted with &lt;math> or {{tl|math}}. Use templates, wiki code formatting, and HTML tags to match the main text, both for inline and displayed formulae.
*For all reactions, the arrow symbol {{User:Hhhippo/sxt|→}} should be used, the equals sign {{User:Hhhippo/!sxt|{{=}}}} is usually wrong.

Examples:
* [[Electron–positron annihilation]]: {{Subatomic particle|Electron}} + {{Subatomic particle|Positron}} → 2{{Subatomic particle|Photon}}.
*[[beta decay|β<sup>−</sup>&nbsp;decay]] as nuclear reaction:
*: {{ComplexNuclide|americium|242|charge=5+}} → {{ComplexNuclide|curium|242|charge=6+}} + {{Subatomic particle|Electron}} + {{Subatomic particle|Electron Antineutrino}}
: and as particle reaction:
:: [[neutron|n]]<sup>0</sup> → [[proton|p]]<sup>+</sup> + {{Subatomic particle|Electron}} + {{Subatomic particle|Electron Antineutrino}}

The [[#Roman versus italic|roman versus italic]] guideline applies to substances:
: {{xt|<math>\displaystyle P = P_0 + 9807\frac{\mathrm{Pa}}{\mathrm m} h \displaystyle 2\rho_{\mathrm{Al}} < \rho_{\mathrm{Fe}}</math>}}
rather than
: {{!xt|<math>\displaystyle P = P_0 + 9807\frac{Pa}{m} h\,.</math>}}

== Sets and spaces ==

=== Number sets ===

Where needed, [[set (mathematics)#Special_sets|standard number sets]] should be set in [[blackboard bold]], not just bold face:
* inline (unicode): {{User:Hhhippo/sxt|ℕ, ℚ, ℤ, ℝ, ℂ}}
* displayed (LaTeX): {{User:Hhhippo/sxt|<math>\mathbb{N, Q, Z, R, C}</math>|title=<nowiki><math>\mathbb{N, Q, Z, R, C}</math></nowiki>}}
* not recommended: {{User:Hhhippo/!sxt|'''N, Q, Z, R, C'''|title=}}

=== Lie groups ===

Symbols for [[Lie group]]s shall be [[Roman type|Roman]], not italic: 
* inline (normal text): {{User:Hhhippo/sxt|SU(''n''), SO(''n''), SL(2, ℂ), U(''n''), O(''n'')}}
* displayed (\mathrm): {{User:Hhhippo/sxt|<math>\mathrm{SU}(n), \mathrm{SO}(n), \mathrm{SL}(2,\mathbb{C}), \mathrm{U}(n), \mathrm{O}(n)</math>|title=<nowiki><math>\mathrm{SU}(n), \mathrm{SO}(n), \mathrm{SL}(2,\mathbb{C}), \mathrm{U}(n), \mathrm{O}(n)</math></nowiki>}}
* not recommended: {{User:Hhhippo/!sxt|<math>SU(n), SO(n), SL(2,\mathbb{C}), U(n), O(n)</math>|title=}}

=== Other ===
* [[Hilbert space]]s: ''H'', <math>\mathcal{H}</math>, or {{math|ℋ}}<!-- any recommendations regarding these? -->

== Prerequisite knowledge==

An article can usually not give a detailed explanation of all concepts and nomenclatures used to explain its topic. Some basic knowledge of physics and mathematics will generally be required of the reader, to an extent depending on the article's subject. However, where appropriate, links to more introductory articles and [[WP:summary style|summary style]] descriptions of the essential concepts should be provided. 

=== Physics ===
A large number of [[Theoretical physics|physical theories]] exist, and compatibility between them varies. Concepts as [[distance]], [[time]] and [[mass]] appear to be universal, although their exact definitions can depend on the subject. Unless an article deals explicitly with these fundamental concepts, it should not explain the meaning of ''distance'', ''time'' or ''mass''.

==== Expected units ====

The following everyday units are presumed to be known and needn't be explained, although ideally linked at least once.
: {| class="wikitable"
|-
! Physical quantity
! [[SI unit]]
! Decimal [[SI prefixes]]
! Common non-SI unit
|-
| [[length]]
| [[metre]] (m)
| [[centimetre]]&nbsp;(cm)
| 
|-
| [[time]]
| [[second]]&nbsp;(s) 
|
| [[minute]]&nbsp;(min), [[hour]]&nbsp;(h),
|-
| [[mass]]
| [[kilogram]]&nbsp;(kg)
| [[gram]]&nbsp;(g)
| 
|-
|}

Other well-known derived quantities include (and these should ideally be linked):
: {| class="wikitable"
|-
! Physical quantity
! [[SI unit]]
! Decimal [[SI prefixes]]
! Common non-SI unit
|-
| [[energy]]
| [[joule|J]]
|
| [[electron volt|eV]]
|-
| [[velocity]]
| [[metre|m]]&sdot;[[second|s]]<sup>−1</sup>
|
|
|-
| [[momentum]]
| [[Newton (unit)|N]]&sdot;[[second|s]] or [[kilogram|kg]]&sdot;[[metre|m]]&sdot;[[second|s]]<sup>−1</sup>
|
|
|-
| [[force]]
| [[Newton (unit)|N]] or [[kilogram|kg]]&sdot;[[metre|m]]<sup>2</sup>&sdot;[[second|s]]<sup>−2</sup>
|
|
|-
| [[pressure]]
| [[Pascal (unit)|Pa]] or [[Newton (unit)|N]]&sdot;[[metre|m]]<sup>−2</sup>
|
|
|-
| etc.
|
|
|
|-
|}

Old non-SI units (such as "[[erg]]", "[[dyne]]", "[[Knot (unit)|knot]]s" etc.), and [[imperial units]], ideally should only to be used for:
* historical relevance,
* within context relevant to those main articles,
* if references (databooks, handbooks, appendices of books etc.) present measurements in terms of those units.

In general, ''SI units'' are usually assumed by most people. When using other unit systems which are extensively employed in practice although may be unfamiliar to laymen, including: 
* [[Gaussian units]] (especially wherever [[electromagnetism|EM]] is applied), and 
* [[natural units]] (especially in ''fundamental'' physics; [[special relativity|SR]], [[general relativity|GR]], [[quantum mechanics|QM]], [[quantum field theory|QFT]], [[particle physics]] etc.), 
it should be explicitly stated they are going to be used before using them. There are several sets of natural units, each with their own applications, so ''which one'' must be clear. Ideally, natural units shouldn't be used, due to lack of familiarity and potential confusion by ''many'' readers. For example: giving masses of [[elementary particle]]s in MeV when the reader thinks of kg (or decimal prefixes thereof) is confusing, a related point is that writing "{{math|''E'' {{=}} ''m''}}", ''without referring to natural units'', is confusing when the reader expects the {{math|''c''<sup>2</sup>}} factor...

{{quotation|'''As a rule of thumb (for natural units):'''
* They ''could'' be used in some calculations or explanations to illustrate ''how'' and ''why'' natural units are better than SI units in the process,
* if the calculation/explanation can easily be done in SI units, ''use SI units'', and not natural units for the sake of it.}}

==== Clarifying the relevant physics ====

Physics is such an enormous subject that an article should specify the relevant branch(es) of it, unless the concept is physically universal. Known ''academic'' paradigms, with usual abbreviations, are:

* '''[[Mechanics]] (all types)'''
* '''[[Classical physics]]:'''
** [[Galilean relativity]], a.k.a. non-relativistic physics
** [[Newtonian mechanics]] (how well-known is [[Analytical mechanics]]?)
** [[Classical field theory]] (includes [[Newton's law of universal gravitation|Newtonian gravitation]] and Maxwell's [[electromagnetism|EM]])
* '''[[Theory of relativity]] (non-Galilean):'''
** [[Special relativity]] (SR)
** [[General relativity]] (GR)
* Non-quantum physics: [[world line]]s and possibly [[classical field]]s, but ''no'' [[wave–particle duality]] or other intrinsic quantum phenomena like [[spin (physics)|particle spin]].
* '''Quantum theory:'''
** [[Quantum mechanics]] (QM, relativistic or non-relativistic)
** [[Quantum field theory]] (QFT, implies QM, SR, background in classical field theory) – not necessary to mention if one of well-known derived theories is used directly:
*** [[Quantum electrodynamics]] (QED)
*** [[Quantum chromodynamics]] (QCD)
* '''[[Particle physics]] (application of relativity and QFT):'''
** Variants of [[Yang–Mills theory]] (which namely?)
** [[Standard Model]]
** [[String theory]] (less known are the specific theories of "[[Heterotic string]]s", "[[D-brane]]s", or "[[M theory]]", etc. so just link to string theory and take it from there?)

The lead of an article should specify the one of these, for example (see the [[wavefunction]] article) anything like:
* {{xt|In [[quantum mechanics]], a branch of [[physics]], a '''wave function''' is ...}}
* {{xt|In [[quantum mechanics]], a '''wave function''' is ...}}
and not simply:
: {{!xt|In [[physics]], a '''wave function''' is ...}}

=== Mathematics ===

==== No abstract notations ====

Any abstract notation which ''requires additional irrelevant explanation'' (i.e. [[set builder notation]], [[List of logic symbols|symbolic logic notations]], ''especially [[Quantifier (logic)#Notation|quantifier notation]]'', others?), are ''not'' to replace ''worded descriptions'' for the sake of compact mathematical statements - they simply create more work in explaining and linking the notations, while contributing no understanding to the ''physics'' at hand.

To exemplify:
* Even if the context becomes abstract, statements like 
*: {{!xt|"''x'' is a number such that {{math|''x'' ∈ ℝ: ''x'' > 0}}, where {{math|∈}} denotes "[[element (mathematics)|element]] of a [[set (mathematics)|set]]", the colon means "such that", and {{math|ℝ}} denotes the [[real number]]s" }}
:are too long, cluttered, and confusing for non-expert mathematicians: simply write 
::{{xt|"''x'' is a [[real number]] greater than and not equal to zero" }}
:since this way ''explains'' the context ''without introducing unfamiliar notations''. 
* Often, integers or half-integers need to be listed (say, listing the number of [[normal mode]]s for a [[standing wave]], the orders of [[diffraction]] in [[physical optics]] and [[condensed matter physics]], or [[quantum number]]s). It's encouraged to simply list the numbers, and if needed followed by an [[ellipsis]] (''three'' dots: ...), like so:
*: {{xt| {{math|''j'' {{=}} 0, {{frac|1|2}}, 1, {{frac|3|2}}...}} }}
: which makes it very clear to anyone that {{math|''j''}} takes those values and the sequence of numbers is infinite. Even though the full [[set builder notation]]:
:: {{!xt| {{math|''j'' ∈ {0, {{frac|1|2}}, 1, {{frac|3|2}}...}, }} or {{math|''j'' ∈ {''n''/2 : ''n'' ∈ ℕ<sub>0</sub>}, }} }} etc.
: is technically more correct, this is actually ''less clearer'' to a typical reader, since the symbols have to be explained by editors and/or read up by readers. 
* Writing compound statements, like the [[zeroth law of thermodynamics]] using logic notation:
*: {{!xt| "The zeroth law can be stated as {{math|(''T<sub>A</sub>'' {{=}} ''T<sub>C</sub>'') &and; (''T<sub>B</sub>'' {{=}} ''T<sub>C</sub>'') ⇒ (''T<sub>A</sub>'' {{=}} ''T<sub>B</sub>'')}} where {{math|&and;}} means "and", {{math|⇒}} denotes "imples", and ''T<sub>A</sub>'', ''T<sub>B</sub>'', ''T<sub>C</sub>'' are the temperatures of objects ''A'', ''B'', ''C''." }}
: may be compact, but is pointless since the notation has to be explained (constituting no thermodynamics). The law can be stated in words:
:: {{xt|"Letting ''T<sub>A</sub>'', ''T<sub>B</sub>'', ''T<sub>C</sub>'' denote the temperatures of objects ''A'', ''B'', ''C'', if ''A'' is in thermal equilibruim with ''C'' (so {{math|''T<sub>A</sub>'' {{=}} ''T<sub>C</sub>''}}), and ''B'' is in thermal equilibruim with ''C'' (so {{math|''T<sub>B</sub>'' {{=}} ''T<sub>C</sub>''}}), then ''A'' and ''B'' are in thermal equilibruim with each other ({{math|''T<sub>A</sub>'' {{=}} ''T<sub>B</sub>''}})." }}

==== Levels of difficulty ====
<!---feel free to change the headings to be "less educational", but not sure how else for now...--->
The tables below (mainly of numbers, [[Operation (mathematics)|operation]]s, and functions required to build formulae) are roughly grouped into three levels of difficulty; school/(advanced) college level, then undergraduate level, finally graduate level (and beyond). Articles which fall into one (or between?) these sections should consider the reader to assume ''some'' familiarity within the scope of the section.

In all cases, the numbers, operations etc.:
* should be linked to the main articles 
* not require any in-depth explanation (a few words or sentence at most).

Of course, other operations not tabulated can be used, provided their use is declared and linked. Most of the operations not tabulated below will be outside the scope of most of physics, such as some non-elementary functions like [[tetration]], super-roots, and [[super-logarithm]]s, and hence no prior knowledge of the reader is required.

===== Elementary level =====

The following are ''always presumed to be known'':
* [[Integer]]s and [[real number]]s, including common constants [[pi|{{math|π}}]] and [[e (mathematical constant)|{{math|''e''}}]], 
* [[decimal]] notation for numbers, including [[scientific notation]] discussed [[#Units and quantities|above]].

When [[complex number]]s are expected, particular examples including;
* [[wave]]s,
* [[electromagnetism]] ([[Electromagnetic radiation|EM radiation]], [[alternating current]]),
* [[quantum mechanics]],
* solutions to [[differential equation]]s,
etc., then [[imaginary unit|{{math|''i''}}]] (or {{math|''j''}}) is presumed to be known too, although the context should state it ''is the imaginary unit'' and not something else, like a summation dummy variable or tensor indices.

{| class=wikitable cellpadding=8px
 !Operation
 !Notation
 !Notes
 |-
 ! colspan=3 align=center |[[Arithmetic]] and [[elementary algebra]]
 |-
 | style="line-height:2.5" |[[Addition]]<br/>[[Subtraction]]<br/>[[Additive inverse]]
 |{{math|''a'' + ''b''}}<br/>{{math|''a'' − ''b''}}<br/>{{math|−''a''}}
 |for scalars, vectors, operators, matrices
 |-
 | style="line-height:2.5" |[[Multiplication]]<br/>[[scalar multiplication|(Scalar, of a vector)]]
 |{{math|''a'' ''b'', ''a''&sdot;''b'', ''a'' &times; ''b''}}<br/>{{math|''λ'' '''v'''}}
 |{{math|''a'', ''b'', ''λ''}} are [[real number]]s, <br/>"vector" {{math|'''v'''}} means element of any linear space
 |-
 |[[Division (mathematics)|Division]]
 |{{math|''a'' / ''b''}} &nbsp; or &nbsp; <math>\displaystyle\frac{a}{b}</math>
 |{{mvar|b}} may be a scalar only
 |-
 |[[Multiplicative inverse]]
 |{{math|''A''<sup>−1<sup>}}
 |for scalars, matrices, operators
 |-
 |[[Absolute value]]
 |{{math|&#124; ''a'' &#124;}}
 | rowspan=2 |including complex numbers
 |-
 |[[±|Plus-minus sign]]
 |{{math|±''a''}}
 |-
 |[[Complex conjugate]]
 |{{math|''{{overline|z}}''}}
 |complex scalars or 2-component spinors<ref>In pure mathematics, for a complex vector&nbsp;{{math|'''v'''}} its conjugate {{math|'''{{overline|v}}'''}} is an element of the [[complex conjugate vector space]]. Although the complex conjugate of a vector is used in physics (for example, in {{math|{{langle}}''ψ''&#124;''A''&#124;''ψ''{{rangle}}}}), the notation with overline is discouraged except for aforementioned two cases.</ref>
 |-
 |[[Square root]]s (and [[nth root]]s?)
 |{{math|{{sqrt|''a''}}, ''p''<sup>1/''q''</sup>}}
 |either {{math|''a'' ≥ 0}} (then {{sqrt|''a''}}&nbsp;≥&nbsp;0),<br/>or defined up to sign
 |-
 |[[Factorial]]
 |{{math| ''n'' !}}
 |Only for integers.
 |-
 |[[Summation]]
 |<math>\displaystyle\sum\limits_k a_k</math>
 |any linear space<br/>only finite sums?
 |-
 |[[Multiplication#Products of sequences|Product]]
 |<math>\displaystyle\prod\limits_k a_k</math>
 |only finite products?
 |-
 ! colspan=3 align=center |[[Elementary function]]s
 |-
 |[[Exponentiation]]
 |{{math|''a''<sup>''b''</sup>}}

(Due to conflict with ''tensor superscripts'', make context clear this ''is exponentiation'')
 | style="line-height:1.5" |for scalar, matrix, operator {{mvar|a}}<br/>for scalar&nbsp;{{mvar|b}} only(?)<br/>either {{math|''a'' ≥ 0}} or {{mvar|b}} must be integer
 |-
 |[[Natural logarithm]]
 |{{math|ln ''a''}}
 |[[multivalued function|multivalued]] unless {{math|''a'' > 0}}
 |-
 |[[Trigonometric functions]]<br/> 
 |All the primary ratios should be known; 

{{math|sin ''x'', cos ''x'', tan ''x'',}}

The secondary are not essential (just reciprocals):

{{math|cosec ''x'', sec ''x'', cot ''x''}}
 |
 |-
 |[[Hyperbolic functions]]
 |All the primary functions should be known; 

{{math|sinh ''x'', cosh ''x'', tanh ''x'',}}

The secondary are not essential (just reciprocals):

{{math|cosech ''x'', sech ''x'', coth ''x''}}
 |
 |-
 ! colspan=3 align=center |Elementary [[calculus]]
 |-
 |Ordinary [[derivative]] (see [[Wikipedia:MOSPHYS#Ratios of differential (infinitesimal) quantities and derivatives|notation above]])
 |{{math|{{sfrac|''d''|''dx''}}''f''(''x'')}}
 |
 |-
 |[[Integral]]s (indefinite, definite, and improper)
 |{{math|<big>&int;</big> ''f''(''x'') ''dx'', <big>&int;</big>{{su|b=''a''|p=''b''}} ''f''(''x'') ''dx''}}
 |
 |-
 ! colspan=3 align=center |''Basic'' [[linear algebra]]
 |-
 |[[Dot product]]
 |{{math|'''a'''&sdot;'''b'''}}
 |[[three-dimensional space|3d]] [[Euclidean vector|Euclidean]] only, unless explained
 |-
 |[[Cross product]]
 |{{math|'''a''' &times; '''b'''}}
 |[[three-dimensional space|3d]] [[Euclidean vector|Euclidean]] only, unless explained
 |-
 |[[Matrix multiplication]]
 |{{math|''A'' ''B''}}
 | Including operations with [[column vector|column-]] and [[row vector]]s
 |-
|}

===== Undergraduate level =====

{| class=wikitable cellpadding=8px
 !Operation
 !Notation
 !Notes
 |-
 ! colspan=3 align=center |[[Multivariable calculus]]
 |-
 |[[Partial derivative]]s, [[Nabla symbol|nabla]]
 |{{math|{{sfrac|∂<sup>2</sup>''F''|∂''y''∂''x''}}, ∇}}
 |
 |-
 |[[Multiple integral]]s (including [[line integral|line]], [[surface integral|surface]], and [[volume integral|volume]] integrals)
 |{{math|<big>&int;&int;&int;</big>{{su|b=''V''|p=}} ψ('''x''') ''dV''}}
 |
 |-
 ! colspan=3 align=center |''Advanced'' linear algebra
 |-
 |[[Exterior product]]
 |{{math|'''a''' &and; '''b'''}}
 |[[Euclidean vector|Euclidean]] only, unless explained
 |-
 |[[Tensor product]]
 |{{math|'''a''' &otimes; '''b''', '''ab'''}}
 |[[Euclidean vector|Euclidean]] only, unless explained
 |-
 |[[Tensor contraction]]
 |{{math|''A''<sup>...''k''...</sup><sub>...</sub> '' B''<sub>...''k''...</sub><sup>...</sup>}}  
 |possibly by multiple indices; see [[#Subscripts and superscripts|above]]
 |-
 |[[Bra-ket notation]]
 |{{math|⟨''ϕ''&#124;}}, &nbsp; {{math|&#124;''ψ''⟩}}, &nbsp; {{math|⟨''ϕ''&#124;''ψ''⟩}}, &nbsp; {{math|⟨''ϕ''&#124;''A''&#124;''ψ''⟩}}
 |see [[#Vectors and vector spaces|above]]
 |-
 |[[Linear operator]] [[function composition|composition]]
 |{{math|''A'' ''B''}}
 |not always distinguished from matrix multiplication
 |-
 | style="line-height:1.5" |[[Conjugate transpose]]<br/>[[Hermitian adjoint]]
 |{{math|''A''<sup>†</sup>}}
 |over complex numbers only,<br />
Usually denoted as {{math|''A''*}} in pure mathematics.
 |-
 |}

Additionally:
* ''Non-elementary functions'' or [[special functions]], namely; the [[gamma function]], [[error function]], [[orthogonal polynomials]], [[Bessel functions]]...
* ''[[Integral transform]]s'' (at least in the simplist forms), including the [[Fourier transform|Fourier]] and [[Laplace transform]]s.

===== Graduate level =====
<!---following needs a LOT more work and expansion, not just my naive conceptions...--->

Very advanced, abstract, and demanding topics, like; 

{| class=wikitable cellpadding=8px
 !Operation
 !Notation
 !Notes
 |-
 |[[Differential form]]s
 |
 |
 |-
 |[[Variational derivative]], [[fractional derivative]], [[covariant derivative]]
 |
 |
 |-
 |[[Functional integration]], [[List of integration and measure theory topics |integration measures]]? 
 | 
 |
 |-
 | ...
 |
 |
 |-
|}

... [[exterior calculus]] on [[manifold]]s, [[analytic function]]s from [[operator (mathematics)|operator]]s, [[operator theory]] on [[Hilbert spaces]], etc., will not be easily understood to the typical reader, and obviously never expected. Such topics need 
* to have enough explanation to make clear the relevance of the mathematics to physics (for instance, why a simpler formulation is not possible?), 
* to be thoroughly linked to the main subject articles containing the details.

== Application of graphics and illustrations ==
<!---to fill--->

== Sidebar and navbox templates ==

{{main|Wikipedia:WikiProject Physics/Templates|Wikipedia:Categories, lists, and navigation templates}}

Templates can be used for linking groups of articles, in the form of: 
* '''sidebars:''' boxes of links with collapsible sections, usually placed in the ''top right corner'' of an article, and 
* '''navboxes:''' boxes of links which are fully collapsible, usually placed at the ''very end'' of the article, even after the [[Wikipedia:Layout#See also section|"see also"]], [[Wikipedia:Citing sources|"references"]], and [[Wikipedia:External links|"external links"]] sections.

A decision at each article should be made for what kind of template of links to use. Sidebars are a matter of debate for their size and layout of links; some favour their use, others oppose or are neutral. Navboxes are usually less problematic due to their compactness. 

* Often, an article is well-served with a picture, diagram, or even an animation (see [[wavefunction]] for a good example), at the very top to provide an immediate visual depiction of what the article says. 
** An image directly corresponding to the specific topic of an article should have priority for putting in the top right corner over a sidebar template. 
** Placing an image in the center, while placing a template in the corner, creates large amounts of whitespace, and the [[WP:TOC|table of contents]] only adds more whitespace. Both can be avoided by having the image floating in the top-right corner and the sidebar below, or replacing the sidebar with a navbox. 
* Some pages on ''abstract'' topics, where it's hard to find an image that's clearly associated with the article, (e.g. articles related to [[string theory]]), may benefit from an "icon" inside a sidebar. This can immediately inform the reader about the substance of the article, while including the links to related articles at the same, hence sidebars may be useful in cases like this.
* Templates with a '''lot''' of links (say, 50 or more<!---Feel free to change the number, but this seems reasonable?--->) are better as footers than as sidebars, since opening the sections of a sidebar makes it extend a long way down the page, and makes the box and article less readable this way. 
* It is legitimate to place navboxes in the "see also" or "references" sections if that's where the article ends. Placing navboxes in "see also" sections is beneficial as they display a large collection of related links in one place with minimum wikicode (only template syntax is needed).
* If the contents of a template only has ''partial relevance'' to the article; they are likely to contribute to [[WP:template creep|template creep]], and hence should not be used.
* If neither are suitable for any reason, the best resort is to just use the [[WP:category|categories]] of the article.

== Conventions in WP articles and sources ==

Aside from units, there are cases where specific choices of mathematical entities have to be made, notably the [[metric tensor]]s in SR and GR, and the representations of the [[gamma matrices]].

Sometimes, reliable and well-established sources use conventions which may lack a clear physical depiction, and WP editors should consider what the best conventions a physics article should have. [[Maxwell's equations#Alternative formulations|Maxwell's equations]] in [[differential form]]s are an example (the 4-current is preferred as a 3-form, but sources (including [[gravitation (book)|''Gravitation'']]) use the 4-current as a 1-form, see the article [[Mathematical descriptions of the electromagnetic field#Differential forms approach|Mathematical descriptions of the electromagnetic field]] for this).

Editors should:
* decide what conventions are the easiest for a reader to follow and for internal consistency, and also state clearly (in a section or footnotes?) the prominent alternative conventions used by other authors,
* decide if [[WP:Editnotices|edit notices]] are necessary (see [[Template:Editnotices/Page/Mathematical descriptions of the electromagnetic field]] for an example) to reflect specific choices made and prevent other editors performing mass-changes to other conventions.

== See also==

* [[Help:displaying a formula]]
* [[Help:template]]

== Footnotes ==
{{reflist}}

== Further reading ==
{{Refbegin}}
* {{cite book|no-tracking=yes|title=AIP style manual|year=1990|publisher=American Institute of Physics|location=New York, N.Y.|isbn=0-88318-642-X|edition=4th |url=http://www.aip.org/pubservs/style/4thed/AIP_Style_4thed.pdf |others=prepared under the direction of the AIP Publication Board}}
* {{cite web|no-tracking=yes|author1=A. Thompson |author2=B. N. Taylor|title=The NIST guide for the use of the International System of Units |url=http://www.nist.gov/pml/pubs/sp811/index.cfm |publisher=The National Institute of Standards and Technology |date=October 5, 2010 |accessdate=February 28, 2013}}
* {{citation
 | editor = University of Chicago Press Staff
 | year = 2010
 | title = The Chicago Manual of Style
 | edition = 16th
 | url = http://www.chicagomanualofstyle.org/home.html
 | publisher = University of Chicago Press
 | isbn = 9780226104201
}}
* {{cite book|no-tracking=yes|editor1-first=Anne |editor1-last=Waldron |editor2-first=Peggy |editor2-last=Judd|editor3-first=Valerie |editor3-last=Miller |title=Physical Review Style and Notation Guide |edition = Revised First |date=June 2011 |url=http://forms.aps.org/author/styleguide.pdf |accessdate=1 March 2013}}
* {{cite book|no-tracking=yes|title=Basic and general concepts and associated terms (VIM)|edition = 3rd|year=2012 |url=http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2012.pdf |publisher=International vocabulary of metrology |accessdate=2 March 2013}}
{{Refend}}