Stochastic quantization: Difference between revisions

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Stochastic quantization serves to quantize [[Euclidean field theory|Euclidean field theories]],<ref name=damgaard>{{cite journal|last=DAMGAARD|first=Poul|author2=Helmuth HUFFEL |title=STOCHASTIC QUANTIZATION|journal=Physics Reports|year=1987|volume=152|issue=5&6|pages=227–398|url=http://homepage.univie.ac.at/helmuth.hueffel/PhysRep.pdf|accessdate=8 March 2013|bibcode = 1987PhR...152..227D |doi = 10.1016/0370-1573(87)90144-X }}</ref> and is used for numerical applications, such as [[numerical simulation]]s of [[Gauge theory|gauge theories]] with [[fermion]]s. This serves to address the problem of [[fermion doubling]] that usually occurs in these numerical calculations.

Stochastic quantization takes advantage of the fact that a Euclidean quantum field theory can be modeled as the [[Thermodynamic equilibrium|equilibrium limit]] of a [[statistical mechanics|statistical mechanical system]] coupled to a [[heat bath]]. In particular, in the [[Path integral formulation|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 function]]s 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 EuclidaenEuclidean path integral measure can also be thought of as the stationary distribution of a stochastic process; hence the name stochastic quantization.

==References==