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Linear Yang–Mills Theory as a Homotopy AQFT

Benini, Marco; Bruinsma, Simen; Schenkel, Alexander

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Marco Benini

Simen Bruinsma


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 ∗-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).


Benini, M., Bruinsma, S., & Schenkel, A. (2019). Linear Yang–Mills Theory as a Homotopy AQFT. Communications in Mathematical Physics, 378, 185–218.

Journal Article Type Article
Acceptance Date Oct 10, 2019
Online Publication Date Dec 5, 2019
Publication Date Dec 5, 2019
Deposit Date Dec 3, 2019
Publicly Available Date Dec 3, 2019
Journal Communications in Mathematical Physics
Print ISSN 0010-3616
Electronic ISSN 1432-0916
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 378
Pages 185–218
Public URL
Publisher URL


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