Lorentz invariance in loop quantum gravity

Sevaghad Shrine Prehistory

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Sevaghad region ... Somiryagad * Little is said about the sanctity of Tanda ...

Sevaghad mahamandhir is located in Kamareddy district in the state of Telangana is located at a distance of 3 km from the town of Ellareddy

Formerly 200 years ago, the region was a dense jungle with no mind wandering ...

Some of our Banjara ancestors Danavat Bhikya Nayak S / Hemla Nayak and Ajmera Sangya Nayak S / Bhojya Nayak migrated with herds of cows and settled here ... then here Somi trees abound and Regadi Due to the presence of soil.the place got the name Somiryagad.

Before 2017 Mission Palli, Thimmappur, Bikkanur, Bollaram, Gandimasanipet near Somiryagad Tanda..5 gram Some of the wadas in the panchayat were merged ... So no development roads , electricity, medicine, education properly Andaka lived in barbarism.

But with the Telangana government setting up the Tandas as special GPs in 2017 .. except for the Vadas in the Bollaram and Gandi Masanipeta areas it has been formed as a Special Somiryagad Gram Panchayat ... since then it has been growing rapidly . Festivals and Pujas together as a whole Celebrating richly ...

All the ancestors of this herd had plenty of cows and cattle.These cattle were grazed by * herdsmen who roamed the whole forest ..

At that time, the herdsmen, who were herdsmen, saw many miracles in this forest.

In many parts of the forest ...Ramapadhas, Siri cows (Lakshmi cow Krishna's beloved Go Mata) are still said to have molded feet ..

There are two or three landmarks in the area where the Great Palace is now under construction .

Apart from this, the ancestors of the place occasionally saw Shankara Mahadev in the forest ... A kilometer away from this herd, in the dense forest, there is a big hill split in two Every day a big tiger comes and there is a sacred Vera.(In the sacred pool of water) Drinking water and lying down in the middle of that cracked hill ... But what kind of harm to the minds or the cattle that go from there Kadata That is why the tiger is the image of Lord Shankara, the area turned to the gods People who believe that it is a holy land ..... We still believe and worship It is our good fortune to be born here ...

In this shrine which is so sacred the people here have been worshiping from the past,but they can not afford it or the real things to the outside world about this area No propaganda or building of a palace .

The temple development committee has been planning to build a mahamandir here at a cost of over Rs 1 crore.

Therefore, devotees, leaders, should make their own donations the government should provide financial assistance from the Department of Revenue .Sevaghad Temple Development Committee.

Sevaghad Temple Development Committee

Grand Unification Epoch

The Grand Unification Epoch is the era in time in the chronology of the universe where no elementary particles existed, and the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions or forces, are merged into one single force. Scientific consensus suggests that 3 minutes after the Big Bang, protons and neutrons began to come together to form the nuclei of simple elements. Loop quantum gravity theories, in contrast, place the origin and the age of elementary particles and the age of Lorentz invariance, beyond 13.799 ± 0.021 billion years ago.

The permanence of Lorentz invariance constants is based on elementary particles and their features. There are eons of time before the Big Bang to build the universe from black holes and older multiverses. There is a selective process that creates features in elementary particles, such as accepting, storing, and giving energy. Lee Smolin's books about loop quantum gravity posit that this theory contains the evolutionary ideas of "reproduction" and "mutation" of universes, and elementary particles, and is formally analogous to models of population biology.

Earlier universes

In the early universes before the Big Bang, there are theories that ''loop quantum gravity loop quantum structures'' formed space. The Lorentz invariance and universal constants describe elementary particles that do not exist yet.

A Fecund universe is a multiverse theory by Lee Smolin about the role of black holes. The theory suggests that black holes and loop quantum gravity connected early universes together, that loop quantum gravity can be pulled into black holes, and that within Fecund universes each new universe has slightly different laws of physics. Because these laws are only slightly different, each is assumed to be like a mutation of the early universes.

Minkowski spacetime

Loop quantum gravity (LQG) is a quantization of a classical Lagrangian classical field theory. It is equivalent to the usual Einstein–Cartan theory in that it leads to the same equations of motion describing general relativity with torsion.

Global Lorentz invariance is broken in LQG just like it is broken in general relativity (unless one is dealing with Minkowski spacetime, which is one particular solution of the Einstein field equations). On the other hand, there has been much talk about possible local and global violations of Lorentz invariance beyond those expected in straightforward general relativity.

Of interest in this connection would be to see whether the LQG analogue of Minkowski spacetime breaks or preserves global Lorentz invariance, and Carlo Rovelli and coworkers have recently been investigating the Minkowski state of LQG using spin foam techniques. These questions will all remain open as long as the classical limits of various LQG models (see below for the sources of variation) cannot be calculated.

Lie algebras and loop quantum gravity

Mathematically LQG is local gauge theory of the self-dual subgroup of the complexified Lorentz group, which is related to the action of the Lorentz group on Weyl spinors commonly used in elementary particle physics. This is partly a matter of mathematical convenience, as it results in a compact group SO(3) or SU(2) as gauge group, as opposed to the non-compact groups SO(3,1) or SL(2.C). The compactness of the Lie group avoids some thus-far unsolved difficulties in the quantization of gauge theories of noncompact lie groups, and is responsible for the discreteness of the area and volume spectra. The theory involving the Immirzi parameter is necessary to resolve an ambiguity in the process of complexification. These are some of the many ways in which different quantizations of the same classical theory can result in inequivalent quantum theories, or even in the impossibility to carry quantization through.

One can't distinguish between SO(3) and SU(2) or between SO(3,1) and SL(2,C) at this level: the respective Lie algebras are the same. In fact, all four groups have the same complexified Lie algebra, which makes matters even more confusing (these subtleties are usually ignored in elementary particle physics). The physical interpretation of the Lie algebra is that of infinitesimally small group transformations, and gauge bosons (such as the graviton) are Lie algebra representations, not Lie group representations. What this means for the Lorentz group is that, for sufficiently small velocity parameters, all four complexified Lie groups are indistinguishable in the absence of matter fields.

To make matters more complicated, it can be shown that a positive cosmological constant can be realized in LQG by replacing the Lorentz group with the corresponding quantum group. At the level of the Lie algebra, this corresponds to what is called q-deforming the Lie algebra, and the parameter q is related to the value of the cosmological constant. The effect of replacing a Lie algebra by a q-deformed version is that the series of its representations is truncated (in the case of the rotation group, instead of having representations labelled by all half-integral spins, one is left with all representations with total spin j less than some constant).

It is entirely possible to formulate LQG in terms of q-deformed Lie algebras instead of ordinary Lie algebras, and in the case of the Lorentz group the result would, again, be indistinguishable for sufficiently small velocity parameters.

Spin networks loop quantum gravity

In the spin-foam formalism, the Barrett–Crane model, which was for a while the most promising state-sum model of 4D Lorentzian quantum gravity, was based on representations of the noncompact groups SO(3,1) or SL(2,C), so the spin foam faces (and hence the spin network edges) were labelled by positive real numbers as opposed to the half-integer labels of SU(2) spin networks.

These and other considerations, including difficulties interpreting what it would mean to apply a Lorentz transformation to a spin network state, led Lee Smolin and others to suggest that spin network states must break Lorentz invariance. Lee Smolin and Joao Magueijo then went on to study doubly special relativity, in which not only there is a constant velocity c but also a constant distance l. They showed that there are nonlinear representations of the Lorentz Lie algebra with these properties (the usual Lorentz group being obtained from a linear representation). Doubly special relativity predicts deviations from the special relativity dispersion relation at large energies (corresponding to small wavelengths of the order of the constant length l in the doubly special theory). Giovanni Amelino-Camelia then proposed that the mystery of ultra-high-energy cosmic rays might be solved by assuming such violations of the special-relativity dispersion relation for photons. No confirmation has been found yet, and this idea is still hypothetical.

Phenomenological (hence, not specific to LQG) constraints on anomalous dispersion relations can be obtained by considering a variety of astrophysical experimental data, of which high-energy cosmic rays are but one part. Current observations are already able to place exceedingly stringent constraints on these phenomenological parameters.