Outputs (56)

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.

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.

Algebraic quantum field theory on spacetimes with timelike boundary (2018)
Journal Article
Benini, M., Dappiaggi, C., & Schenkel, A. (2018). Algebraic quantum field theory on spacetimes with timelike boundary. Annales Henri Poincaré, 19(8), 2401-2433. https://doi.org/10.1007/s00023-018-0687-1

We analyze quantum field theories on spacetimes M with timelike boundary from a model independent perspective. We construct an adjunction which describes a universal extension to the whole spacetime M of theories defined only on the interior intM. Th... Read More about Algebraic quantum field theory on spacetimes with timelike boundary.

The stack of Yang-Mills fields on Lorentzian manifolds (2018)
Journal Article
Benini, M., Schenkel, A., & Schreiber, U. (2018). The stack of Yang-Mills fields on Lorentzian manifolds. Communications in Mathematical Physics, 359(2), 765-820. https://doi.org/10.1007/s00220-018-3120-1

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 Yang-Mills Cauchy problem and show that its well-posed... Read More about The stack of Yang-Mills fields on Lorentzian manifolds.

Quantum field theories on categories fibered in groupoids (2017)
Journal Article
Benini, M., & Schenkel, A. (2017). Quantum field theories on categories fibered in groupoids. Communications in Mathematical Physics, 356(1), 19-64. https://doi.org/10.1007/s00220-017-2986-7

We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geome... Read More about Quantum field theories on categories fibered in groupoids.

Global anomalies on Lorentzian space-times (2017)
Journal Article
Schenkel, A., & Zahn, J. (2017). Global anomalies on Lorentzian space-times. Annales Henri Poincaré, 18(8), 2693-2714. https://doi.org/10.1007/s00023-017-0590-1

We formulate an algebraic criterion for the presence of global anomalies on globally hyperbolic space-times in the framework of locally covariant field theory. We discuss some consequences and check that it reproduces the well-known global SU(2) anom... Read More about Global anomalies on Lorentzian space-times.

Mapping spaces and automorphism groups of toric noncommutative spaces (2017)
Journal Article
Barnes, G. E., Schenkel, A., & Szabo, R. J. (2017). Mapping spaces and automorphism groups of toric noncommutative spaces. Letters in Mathematical Physics, 107(9), 1591-1628. https://doi.org/10.1007/s11005-017-0957-8

We develop a sheaf theory approach to toric noncommutative geometry which allows us to formalize the concept of mapping spaces between two toric noncommutative spaces. As an application we study the 'internalized' automorphism group of a toric noncom... Read More about Mapping spaces and automorphism groups of toric noncommutative spaces.

Wavefront sets and polarizations on supermanifolds (2017)
Journal Article
Dappiaggi, C., Gimperlein, H., Murro, S., & Schenkel, A. (2017). Wavefront sets and polarizations on supermanifolds. Journal of Mathematical Physics, 58(2), Article 23504. https://doi.org/10.1063/1.4975213

In this paper we develop the foundations for microlocal analysis on supermanifolds. Making use of pseudodifferential operators on supermanifolds as introduced by Rempel and Schmitt, we define a suitable notion of super wavefront set for superdistribu... Read More about Wavefront sets and polarizations on supermanifolds.

Non-existence of natural states for Abelian Chern–Simons theory (2017)
Journal Article
Dappiaggi, C., Murro, S., & Schenkel, A. (2017). Non-existence of natural states for Abelian Chern–Simons theory. Journal of Geometry and Physics, 116, 119-123. https://doi.org/10.1016/j.geomphys.2017.01.015

We give an elementary proof that Abelian Chern-Simons theory, described as a functor from oriented surfaces to C*-algebras, does not admit a natural state. Non-existence of natural states is thus not only a phenomenon of quantum field theories on Lor... Read More about Non-existence of natural states for Abelian Chern–Simons theory.