Covariant SPDEs and Quantum Field Structures

TL;DR

This paper investigates covariant stochastic PDEs across dimensions, identifying a class whose solutions can be analytically continued to Minkowski space, producing covariant Wightman distributions consistent with key quantum field theory axioms.

Contribution

It introduces a special class of covariant SPDEs and proves their solutions can be analytically continued to Minkowski space, satisfying quantum field theory axioms.

Findings

Solutions yield covariant, local Wightman distributions

Analytic continuation to Minkowski space is established

Distributions obey the spectral and locality axioms

Abstract

Covariant stochastic partial differential equations are studied in any dimension. A special class of such equations is selected and it is proven that the solutions can be analytically continued to Minkowski space-time yielding tempered Wightman distributions which are covariant, obey the locality axiom and a weak form of the spectral axiom. Key words: stochastic partial differential equations, white noise, covariant Markov generalized random fields, Euclidean QFT, Schwinger functions, Wightman distributions