# Linear Yang-Mills theory as a homotopy AQFT

## TL;DR

This paper develops a homotopy algebraic quantum field theory framework for linear Yang-Mills theory, revealing richer structures including gauge fields, ghosts, and antifields, and connecting to classical solutions via retarded/advanced trivializations.

## Contribution

It introduces a homotopy AQFT construction for linear Yang-Mills theory that captures gauge symmetries and BRST/BV structures, extending standard quantization methods.

## Key findings

- Reproduces BRST/BV field content for Yang-Mills
- Establishes a homotopy AQFT framework with retarded/advanced trivializations
- Connects the quantization to classical solution complexes

## Abstract

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).