All Outputs (59)

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.

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.

Differential cohomology and locally covariant quantum field theory (2016)
Journal Article
Becker, C., Schenkel, A., & Szabo, R. J. (2017). Differential cohomology and locally covariant quantum field theory. Reviews in Mathematical Physics, 29(1), Article 1750003. https://doi.org/10.1142/S0129055X17500039

We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental... Read More about Differential cohomology and locally covariant quantum field theory.

Poisson algebras for non-linear field theories in the Cahiers topos (2016)
Journal Article
Benini, M., & Schenkel, A. (2017). Poisson algebras for non-linear field theories in the Cahiers topos. Annales Henri Poincaré, 18(4), 1435-1464. https://doi.org/10.1007/s00023-016-0533-2

We develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework the solution space of the field equation carries a natural smoot... Read More about Poisson algebras for non-linear field theories in the Cahiers topos.

Working with Nonassociative Geometry and Field Theory (2016)
Journal Article
E. Barnes, G., Schenkel, A., & J. Szabo, R. (2016). Working with Nonassociative Geometry and Field Theory. Proceedings of Science, 263, https://doi.org/10.22323/1.263.0081

We review aspects of our formalism for differential geometry on noncommutative and nonassociative spaces which arise from cochain twist deformation quantization of manifolds. We work in the simplest setting of trivial vector bundles and flush out the... Read More about Working with Nonassociative Geometry and Field Theory.

Noncommutative principal bundles through twist deformation (2016)
Journal Article
Aschieri, P., Bieliavsky, P., Pagani, C., & Schenkel, A. (2017). Noncommutative principal bundles through twist deformation. Communications in Mathematical Physics, 352(1), 287-344. https://doi.org/10.1007/s00220-016-2765-x

We construct noncommutative principal bundles deforming principal bundles with a Drinfeld twist (2-cocycle). If the twist is associated with the structure group then we have a deformation of the fibers. If the twist is associated with the automorphis... Read More about Noncommutative principal bundles through twist deformation.

Abelian duality on globally hyperbolic spacetimes (2016)
Journal Article
Becker, C., Benini, M., Schenkel, A., & Szabo, R. J. (2017). Abelian duality on globally hyperbolic spacetimes. Communications in Mathematical Physics, 349(1), 361-392. https://doi.org/10.1007/s00220-016-2669-9

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 of globally hyperbolic Lorentzian manifolds. Our app... Read More about Abelian duality on globally hyperbolic spacetimes.

Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature (2016)
Journal Article
Barnes, G. E., Schenkel, A., & Szabo, R. J. (2016). Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature. Journal of Geometry and Physics, 106, 234-255. https://doi.org/10.1016/j.geomphys.2016.04.005

We continue our systematic development of noncommutative and nonassociative differential geometry internal to the representation category of a quasitriangular quasi-Hopf algebra. We describe derivations, differential operators, differential calculi a... Read More about Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature.

Supergeometry in locally covariant quantum field theory (2015)
Journal Article
Hack, T., Hanisch, F., & Schenkel, A. (2016). Supergeometry in locally covariant quantum field theory. Communications in Mathematical Physics, 342(2), 615-673. https://doi.org/10.1007/s00220-015-2516-4

In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a... Read More about Supergeometry in locally covariant quantum field theory.

Homotopy colimits and global observables in Abelian gauge theory (2015)
Journal Article
Benini, M., Schenkel, A., & Szabo, R. J. (2015). Homotopy colimits and global observables in Abelian gauge theory. Letters in Mathematical Physics, 105(9), https://doi.org/10.1007/s11005-015-0765-y

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 by using techniques from homotopy theory. The extension prescription... Read More about Homotopy colimits and global observables in Abelian gauge theory.

Nonassociative geometry in quasi-Hopf representation categories I: bimodules and their internal homomorphisms (2014)
Journal Article
Barnes, G. E., Schenkel, A., & Szabo, R. J. (2015). Nonassociative geometry in quasi-Hopf representation categories I: bimodules and their internal homomorphisms. Journal of Geometry and Physics, 89, 111-152. https://doi.org/10.1016/j.geomphys.2014.12.005

We systematically study noncommutative and nonassociative algebras A and their bimodules as algebras and bimodules internal to the representation category of a quasitriangular quasi-Hopf algebra. We enlarge the morphisms of the monoidal category of A... Read More about Nonassociative geometry in quasi-Hopf representation categories I: bimodules and their internal homomorphisms.

Noncommutative connections on bimodules and Drinfeld twist deformation (2014)
Journal Article
Aschieri, P., & Schenkel, A. (2014). Noncommutative connections on bimodules and Drinfeld twist deformation. Advances in Theoretical and Mathematical Physics, 18(3), 513-612

Given a Hopf algebra H, we study modules and bimodules over an algebra A that carry an H-action, as well as their morphisms and connections. Bimodules naturally arise when considering noncommutative analogues of tensor bundles. For quasitriangular Ho... Read More about Noncommutative connections on bimodules and Drinfeld twist deformation.