Stochastic quantization

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

  1. ↑ Nelson, E. (1966). "Derivation of the Schrödinger Equation from Newtonian Mechanics". Physical Review. 150 (4): 1079. Bibcode:1966PhRv..150.1079N. doi:10.1103/PhysRev.150.1079.; Fényes, I. (1952). "Eine wahrscheinlichkeitstheoretische Begründung und Interpretation der Quantenmechanik". Zeitschrift für Physik. 132: 81–10. Bibcode:1952ZPhy..132...81F. doi:10.1007/BF01338578.; De La Peña-Auerbach, L. (1967). "A simple derivation of the Schroedinger equation from the theory of Markoff processes". Physics Letters A. 24 (11): 603–604. Bibcode:1967PhLA...24..603D. doi:10.1016/0375-9601(67)90639-1.
  2. ↑ Parisi, G; Y.-S. Wu (1981). "Perturbation theory without gauge fixing". Sci. Sinica. 24: 483.
  3. ↑ 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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