All Outputs (7)

Cheeger-Simons differential characters with compact support and Pontryagin duality (2019)
Journal Article
Becker, C., Benini, M., Schenkel, A., & Szabo, R. J. (2019). Cheeger-Simons differential characters with compact support and Pontryagin duality. Communications in Analysis and Geometry, 27(7), 1473–1522

By adapting the Cheeger-Simons approach to differential cohomology, we establish a notion of differential cohomology with compact support. We show that it is functorial with respect to open embeddings and that it fits into a natural diagram of exact... Read More about Cheeger-Simons differential characters with compact support and Pontryagin duality.

Linear Yang–Mills Theory as a Homotopy AQFT (2019)
Journal Article
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

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 Gr... Read More about Linear Yang–Mills Theory as a Homotopy AQFT.

Model-independent comparison between factorization algebras and algebraic quantum field theory on Lorentzian manifolds (2019)
Journal Article
Benini, M., Perin, M., & Schenkel, A. (2020). Model-independent comparison between factorization algebras and algebraic quantum field theory on Lorentzian manifolds. Communications in Mathematical Physics, 377(2), 971-997. https://doi.org/10.1007/s00220-019-03561-x

This paper investigates the relationship between algebraic quantum field theories and factorization algebras on globally hyperbolic Lorentzian manifolds. Functorial constructions that map between these two types of theories in both directions are dev... Read More about Model-independent comparison between factorization algebras and algebraic quantum field theory on Lorentzian manifolds.

Algebraic field theory operads and linear quantization (2019)
Journal Article
Bruinsma, S., & Schenkel, A. (2019). Algebraic field theory operads and linear quantization. Letters in Mathematical Physics, 109(11), 2531-2570. https://doi.org/10.1007/s11005-019-01195-7

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 operad. A novel feature of our framework is that it gi... Read More about Algebraic field theory operads and linear quantization.

Higher Structures in Algebraic Quantum Field Theory: LMS/EPSRC Durham Symposium on Higher Structures in M‐Theory (2019)
Journal Article
Benini, M., & Schenkel, A. (2019). Higher Structures in Algebraic Quantum Field Theory: LMS/EPSRC Durham Symposium on Higher Structures in M‐Theory. Fortschritte der Physik / Progress of Physics, 67(8-9), 1-24. https://doi.org/10.1002/prop.201910015

A brief overview of the recent developments of operadic and higher categorical techniques in algebraic quantum field theory is given. The relevance of such mathematical structures for the description of gauge theories is discussed.

Involutive categories, colored * -operads and quantum field theory (2019)
Journal Article
Benini, M., Schenkel, A., & Woike, L. (2019). Involutive categories, colored * -operads and quantum field theory. Theory and Applications of Categories, 34(2), 13-57

Involutive category theory provides a flexible framework to describe involutive structures on algebraic objects, such as anti-linear involutions on complex vector spaces. Motivated by the prominent role of involutions in quantum (field) theory, we de... Read More about Involutive categories, colored * -operads and quantum field theory.

Homotopy theory of algebraic quantum field theories (2019)
Journal Article
Benini, M., Schenkel, A., & Woike, L. (2019). Homotopy theory of algebraic quantum field theories. Letters in Mathematical Physics, 109(7), 1487-1532. https://doi.org/10.1007/s11005-018-01151-x

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 category of such theories carries a canonical model stru... Read More about Homotopy theory of algebraic quantum field theories.