# Linear Yang-Mills theory as a homotopy AQFT

June 03, 2019

It is observed that the shifted Poisson structure (antibracket) on the
solution complex of Klein-Gordon and linear Yang-Mills theory on globally
hyperbolic Lorentzian manifolds admits retarded/advanced trivializations
(analogs of retarded/advanced Green's operators). Quantization of the
associated unshifted Poisson structure determines a unique (up to equivalence)
homotopy algebraic quantum field theory (AQFT), i.e. a functor that assigns
differential graded $\ast$-algebras of observables and fulfills homotopical
analogs of the AQFT axioms. For Klein-Gordon theory the construction is
equivalent to the standard one, while for linear Yang-Mills it is richer and
reproduces the BRST/BV field content (gauge fields, ghosts and antifields).

open access link

@article{Benini:2019hoc,
author = "Benini, Marco and Bruinsma, Simen and Schenkel,
Alexander",
title = "{Linear Yang-Mills theory as a homotopy AQFT}",
year = "2019",
eprint = "1906.00999",
archivePrefix = "arXiv",
primaryClass = "math-ph",
reportNumber = "ZMP-HH/19-10, Hamburger Beitraege zur Mathematik Nr. 789",
SLACcitation = "%%CITATION = ARXIV:1906.00999;%%"
}

Keywords:

algebraic quantum field theory, locally covariant quantum field theory, Gauge theory, derived critical locus, homotopical algebra, chain complexes, BRST/BV formalism