# Relative Cauchy evolution for linear homotopy AQFTs

Simen Bruinsma, Christopher J. Fewster, Alexander Schenkel
August 24, 2021
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.

Keywords:
algebraic quantum field theory, relative Cauchy evolution, Gauge theory, homotopical algebra, chain complexes, BRST/BV formalism