TY - JOUR

T1 - From stochastic quantization to bulk quantization

T2 - Schwinger-dyson equations and s-matrix

AU - Baulieu, Laurent

AU - Zwanziger, Daniel

N1 - Publisher Copyright:
© 2018 Elsevier B.V., All rights reserved.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2001

Y1 - 2001

N2 - In stochastic quantization, ordinary 4-dimensional Euclidean quantum field theory is expressed as a functional integral over fields in 5 dimensions with a fictitious 5th time. However a broader framework, which we call“bulk quantization”, is required for extension to fermions, and for the increased power afforded by the higher symmetry of the 5-dimensional action that is topological when expressed in terms of auxiliary fields. Within the broader framework, we give a direct proof by means of Schwinger-Dyson equations that a time-slice of the 5-dimensional theory is equivalent to the usual 4-dimensional theory. The proof does not rely on the conjecture that the relevant stochastic process relaxes to an equilibrium distribution. Rather, it depends on the higher symmetry of the 5-dimensional action which includes a BRST-type topological invariance, and invariance under translation and inversion in the 5-th time. We express the physical S-matrix directly in terms of the truncated 5-dimensional correlation functions, for which “going off the mass-shell” means going from the 3 physical degrees of freedom to 5 independent variables. We derive the Landau-Cutokosky rules of the 5-dimensional theory which include the physical unitarity relation.

AB - In stochastic quantization, ordinary 4-dimensional Euclidean quantum field theory is expressed as a functional integral over fields in 5 dimensions with a fictitious 5th time. However a broader framework, which we call“bulk quantization”, is required for extension to fermions, and for the increased power afforded by the higher symmetry of the 5-dimensional action that is topological when expressed in terms of auxiliary fields. Within the broader framework, we give a direct proof by means of Schwinger-Dyson equations that a time-slice of the 5-dimensional theory is equivalent to the usual 4-dimensional theory. The proof does not rely on the conjecture that the relevant stochastic process relaxes to an equilibrium distribution. Rather, it depends on the higher symmetry of the 5-dimensional action which includes a BRST-type topological invariance, and invariance under translation and inversion in the 5-th time. We express the physical S-matrix directly in terms of the truncated 5-dimensional correlation functions, for which “going off the mass-shell” means going from the 3 physical degrees of freedom to 5 independent variables. We derive the Landau-Cutokosky rules of the 5-dimensional theory which include the physical unitarity relation.

KW - BRST Quantization

KW - Non-perturbative Effects

KW - QCD

KW - Renormalization Regularization and Renormalons

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U2 - 10.1088/1126-6708/2001/08/016

DO - 10.1088/1126-6708/2001/08/016

M3 - Article

AN - SCOPUS:33745047340

VL - 5

SP - 1

EP - 24

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 8

ER -