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arXiv · 1906.00999

Linear Yang-Mills theory as a homotopy AQFT

Marco Benini·Simen Bruinsma·Alexander Schenkel
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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).

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Marco Benini, Simen Bruinsma, Alexander Schenkel. 2019-12-03. Linear Yang-Mills theory as a homotopy AQFT. https://doi.org/10.1007/s00220-019-03640-z

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