Stochastic quantization
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In physics, stochastic quantization is a method for modelling quantum mechanics, introduced by Edward Nelson in 1966,[1] and streamlined by Parisi and Wu.[2]
It serves to quantize Euclidean field theories,[3] and is used for numerical applications, such as numerical simulations of gauge theories with fermions.
Stochastic quantization takes advantage of the fact that a Euclidean quantum field theory can be modeled as the equilibrium limit of a statistical mechanical system coupled to a heat bath. In particular, in the path integral representation of a Euclidean quantum field theory, the path integral measure is closely related to the Boltzmann distribution of a statistical mechanical system in equilibrium. In this relation, Euclidean Green's functions become correlation functions in the statistical mechanical system. A statistical mechanical system in equilibrium can be modeled, via the ergodic hypothesis, as the stationary distribution of a stochastic process. Then the Euclidean path integral measure can also be thought of as the stationary distribution of a stochastic process; hence the name stochastic quantization.
References
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|doi=10.1103/PhysRev.150.1079instead.; Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1007/BF01338578, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with|doi=10.1007/BF01338578instead.; Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1016/0375-9601(67)90639-1, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with|doi=10.1016/0375-9601(67)90639-1instead. - ^ Parisi, G; Y.-S. Wu (1981). Sci. Sinica. 24: 483.
{{cite journal}}: Missing or empty|title=(help) - ^ DAMGAARD, Poul; Helmuth HUFFEL (1987). "STOCHASTIC QUANTIZATION" (PDF). Physics Reports. 152 (5&6): 227–398. Bibcode:1987PhR...152..227D. doi:10.1016/0370-1573(87)90144-X. Retrieved 8 March 2013.
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