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Investigation of Green Functions and the Parisi‐Wu Quantization Method in Background Stochastic Fields
Author(s) -
Dineykhan M.,
Efimov G. V.,
Namsrai Kh.
Publication year - 1991
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190390402
Subject(s) - stochastic quantization , white noise , quantization (signal processing) , langevin equation , quantum nonlocality , physics , mathematics , scalar field , stochastic process , statistical physics , quantum field theory , mathematical physics , path integral formulation , quantum , quantum mechanics , quantum entanglement , statistics , algorithm
Abstract In this review we present variational and stochastic method of evaluating functional integrals and quantization of different fields (scalar, electromagnetic and Yang‐Mills gauge ones). These methods are applied to the study of the asymptotic behavior of the scalar particle Green functions in stochastic fields and to the construction of a finite quantum field theory by means of the nonlocal white noise‐like background stochastic fields in the scheme due to Parisi and Wu. In our mathematical prescription the white noise‐like field plays a double role, it controls the quantum behavior of the theory and at the same time it carries nonlocality in stochastic Langevin‐type equations. We also introduce stochasticity of the space‐time metric in the context of stochastic background field and discuss its consequences.