Linear Yang-Mills theory as a homotopy AQFT

Marco Benini, Simen Bruinsma, Alexander Schenkel
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).
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@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;%%" }

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