Linear Yang-Mills theory as a homotopy AQFT

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).

arXiv comment31 pages - v2: Final version to appear in Communications in Mathematical Physics

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Cited by in corpus (12)

• Categorification of algebraic quantum field theories
• Snowmass White Paper: The Quest to Define QFT
• A Lorentzian renormalisation group equation for gauge theories
• Strictification theorems for the homotopy time-slice axiom
• Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory
• Green hyperbolic complexes on Lorentzian manifolds
• Relative Cauchy evolution for linear homotopy AQFTs
• Homotopy theory of net representations
• The linear CS/WZW bulk/boundary system in AQFT
• On the equivalence of AQFTs and prefactorization algebras
• Classical BV formalism for group actions
• Extended Field Theories as higher Kaluza-Klein theories