Linear Yang–Mills Theory as a Homotopy AQFT

@article{Benini2019LinearYT,
  title={Linear Yang–Mills Theory as a Homotopy AQFT},
  author={Marco Benini and Simen Bruinsma and Alexander Schenkel},
  journal={Communications in Mathematical Physics},
  year={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 $$*$$ ∗ -algebras of observables… 
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References

SHOWING 1-10 OF 62 REFERENCES
Renormalized Quantum Yang-Mills Fields in Curved Spacetime
We present a proof that the quantum Yang–Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian
The Stack of Yang–Mills Fields on Lorentzian Manifolds
We provide an abstract definition and an explicit construction of the stack of non-Abelian Yang–Mills fields on globally hyperbolic Lorentzian manifolds. We also formulate a stacky version of the
Abelian Duality on Globally Hyperbolic Spacetimes
We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger–Simons differential cohomology on the category
Homotopy theory of algebraic quantum field theories
Motivated by gauge theory, we develop a general framework for chain complex-valued algebraic quantum field theories. Building upon our recent operadic approach to this subject, we show that the
Cohomology with Causally Restricted Supports
De Rham cohomology with spacelike compact and timelike compact supports has recently been noticed to be of importance for understanding the structure of classical and quantum Maxwell theory on curved
Homotopy Colimits and Global Observables in Abelian Gauge Theory
We study chain complexes of field configurations and observables for Abelian gauge theory on contractible manifolds, and show that they can be extended to non-contractible manifolds using techniques
Wave Equations on Lorentzian Manifolds and Quantization
This book provides a detailed introduction to linear wave equations on Lorentzian manifolds (for vector-bundle valued fields). After a collection of preliminary material in the first chapter one
Algebraic field theory operads and linear quantization
We generalize the operadic approach to algebraic quantum field theory [arXiv:1709.08657] to a broader class of field theories whose observables on a spacetime are algebras over any single-colored
Operads for algebraic quantum field theory
We construct a colored operad whose category of algebras is the category of algebraic quantum field theories. This is achieved by a construction that depends on the choice of a category, whose
Quantized Abelian Principal Connections on Lorentzian Manifolds
We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work
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