SPDEs leading to local, relativistic quantum vector fields with indefinite metric and nontrivial S-matrix

TL;DR

This paper reviews the construction of local, relativistic quantum vector fields via analytic continuation of Euclidean solutions to covariant SPDEs, introducing new Gaussian noise terms to achieve nontrivial scattering.

Contribution

It introduces a novel formulation of SPDEs with Gaussian noise that simplifies the construction of relativistic quantum fields with nontrivial S-matrix.

Findings

New SPDE formulation avoids re-defining two-point functions

Constructs asymptotic states and describes scattering

Provides conditions for nontrivial, well-defined scattering

Abstract

In this article we review the construction of local, relativistic quantum vector fields by analytic continuation of Euclidean vector fields obtained as solutions of covariant SPDEs. We revise the formulation of such SPDEs by introducing new Gaussian noise terms -- a procedure which avoids the re-definition of the two point functions needed in previous approaches in order to obtain relativistic fields with nontrivial scattering. We describe the construction of asymptotic states and the scattering of the analytically continued solutions of these new SPDEs and we give precise conditions for nontrivial and well-defined scattering.