Relative Cauchy evolution for linear homotopy AQFTs

TL;DR

This paper introduces a new framework for analyzing the evolution of homotopy algebraic quantum field theories, demonstrating its application to linear Yang-Mills theory and recovering the stress-energy tensor.

Contribution

It develops a relative Cauchy evolution concept for homotopy AQFTs and proves a rectification theorem to strictify the homotopy time-slice axiom.

Findings

Established a relative Cauchy evolution for homotopy AQFTs

Proved a rectification theorem for the homotopy time-slice axiom

Applied the framework to linear Yang-Mills theory, recovering the stress-energy tensor

Abstract

This paper develops a concept of relative Cauchy evolution for the class of homotopy algebraic quantum field theories (AQFTs) that are obtained by canonical commutation relation quantization of Poisson chain complexes. The key element of the construction is a rectification theorem proving that the homotopy time-slice axiom, which is a higher categorical relaxation of the time-slice axiom of AQFT, can be strictified for theories in this class. The general concept is illustrated through a detailed study of the relative Cauchy evolution for the homotopy AQFT associated with linear Yang-Mills theory, for which the usual stress-energy tensor is recovered.