Linear Yang–Mills Theory as a Homotopy AQFT

Benini, Marco; Bruinsma, Simen; Schenkel, Alexander

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 ∗-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).

Citation

Benini, M., Bruinsma, S., & Schenkel, A. (2019). Linear Yang–Mills Theory as a Homotopy AQFT. Communications in Mathematical Physics, 378, 185–218. https://doi.org/10.1007/s00220-019-03640-z

• 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
• DOI: https://doi.org/10.1007/s00220-019-03640-z
• Public URL: https://nottingham-repository.worktribe.com/output/3465499
• Publisher URL: https://link.springer.com/article/10.1007%2Fs00220-019-03640-z