Outputs (60)

Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory (2024)
Journal Article
Benini, M., Musante, G., & Schenkel, A. (2024). Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory. Letters in Mathematical Physics, 114(1), Article 36. https://doi.org/10.1007/s11005-024-01784-1

We construct and compare two alternative quantizations, as a time-orderable prefactorization algebra and as an algebraic quantum field theory valued in cochain complexes, of a natural collection of free BV theories on the category of m-dimensional gl... Read More about Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory.

Green Hyperbolic Complexes on Lorentzian Manifolds (2023)
Journal Article
Benini, M., Musante, G., & Schenkel, A. (2023). Green Hyperbolic Complexes on Lorentzian Manifolds. Communications in Mathematical Physics, 403, 699-744. https://doi.org/10.1007/s00220-023-04807-5

We develop a homological generalization of Green hyperbolic operators, called Green hyperbolic complexes, which cover many examples of derived critical loci for gauge-theoretic quadratic action functionals in Lorentzian signature. We define Green hyp... Read More about Green Hyperbolic Complexes on Lorentzian Manifolds.

The Linear CS/WZW Bulk/Boundary System in AQFT (2023)
Journal Article
Benini, M., Grant-Stuart, A., & Schenkel, A. (2024). The Linear CS/WZW Bulk/Boundary System in AQFT. Annales Henri Poincaré, 25, 2251-2294. https://doi.org/10.1007/s00023-023-01346-6

This paper constructs in the framework of algebraic quantum field theory (AQFT) the linear Chern–Simons/Wess–Zumino–Witten system on a class of 3-manifolds M whose boundary ∂M is endowed with a Lorentzian metric. It is proven that this AQFT is equiva... Read More about The Linear CS/WZW Bulk/Boundary System in AQFT.

Strictification theorems for the homotopy time-slice axiom (2023)
Journal Article
Benini, M., Carmona, V., & Schenkel, A. (2023). Strictification theorems for the homotopy time-slice axiom. Letters in Mathematical Physics, 113(1), Article 20. https://doi.org/10.1007/s11005-023-01647-1

It is proven that the homotopy time-slice axiom for many types of algebraic quantum field theories (AQFTs) taking values in chain complexes can be strictified. This includes the cases of Haag–Kastler-type AQFTs on a fixed globally hyperbolic Lorentzi... Read More about Strictification theorems for the homotopy time-slice axiom.

BV quantization of dynamical fuzzy spectral triples (2022)
Journal Article
Gaunt, J., Nguyen, H., & Schenkel, A. (2022). BV quantization of dynamical fuzzy spectral triples. Journal of Physics A: Mathematical and Theoretical, 55(47), Article 474004. https://doi.org/10.1088/1751-8121/aca44f

This paper provides a systematic study of gauge symmetries in the dynamical fuzzy spectral triple models for quantum gravity that have been proposed by Barrett and collaborators. We develop both the classical and the perturbative quantum BV formalism... Read More about BV quantization of dynamical fuzzy spectral triples.

A Skeletal Model for 2d Conformal AQFTs (2022)
Journal Article
Benini, M., Giorgetti, L., & Schenkel, A. (2022). A Skeletal Model for 2d Conformal AQFTs. Communications in Mathematical Physics, 395(1), 269-298. https://doi.org/10.1007/s00220-022-04428-4

A simple model for the localization of the category CLoc2 of oriented and time-oriented globally hyperbolic conformal Lorentzian 2-manifolds at all Cauchy morphisms is constructed. This provides an equivalent description of 2-dimensional conformal al... Read More about A Skeletal Model for 2d Conformal AQFTs.

Relative Cauchy Evolution for Linear Homotopy AQFTs (2022)
Journal Article
Bruinsma, S., Fewster, C. J., & Schenkel, A. (2022). Relative Cauchy Evolution for Linear Homotopy AQFTs. Communications in Mathematical Physics, 392(2), 621-657. https://doi.org/10.1007/s00220-022-04352-7

This paper develops a concept of relative Cauchy evolution for the class of homotopy algebraic quantum field theories (AQFTs) that are obtained by canonical commutation relation quantization of Poisson chain complexes. The key element of the construc... Read More about Relative Cauchy Evolution for Linear Homotopy AQFTs.

Homotopical Analysis of 4d Chern-Simons Theory and Integrable Field Theories (2022)
Journal Article
Benini, M., Schenkel, A., & Vicedo, B. (2022). Homotopical Analysis of 4d Chern-Simons Theory and Integrable Field Theories. Communications in Mathematical Physics, 389, 1417-1443. https://doi.org/10.1007/s00220-021-04304-7

This paper provides a detailed study of 4-dimensional Chern-Simons theory on R2× CP1 for an arbitrary meromorphic 1-form ω on CP1. Using techniques from homotopy theory, the behaviour under finite gauge transformations of a suitably regularised versi... Read More about Homotopical Analysis of 4d Chern-Simons Theory and Integrable Field Theories.

Smooth 1-Dimensional Algebraic Quantum Field Theories (2021)
Journal Article
Benini, M., Perin, M., & Schenkel, A. (2022). Smooth 1-Dimensional Algebraic Quantum Field Theories. Annales Henri Poincaré, 23, 2069-2111. https://doi.org/10.1007/s00023-021-01132-2

This paper proposes a refinement of the usual concept of algebraic quantum field theories (AQFTs) to theories that are smooth in the sense that they assign to every smooth family of spacetimes a smooth family of observable algebras. Using stacks of c... Read More about Smooth 1-Dimensional Algebraic Quantum Field Theories.

Batalin–Vilkovisky quantization of fuzzy field theories (2021)
Journal Article
Nguyen, H., Schenkel, A., & Szabo, R. J. (2021). Batalin–Vilkovisky quantization of fuzzy field theories. Letters in Mathematical Physics, 111(6), Article 149. https://doi.org/10.1007/s11005-021-01490-2

We apply the modern Batalin–Vilkovisky quantization techniques of Costello and Gwilliam to noncommutative field theories in the finite-dimensional case of fuzzy spaces. We further develop a generalization of this framework to theories that are equiva... Read More about Batalin–Vilkovisky quantization of fuzzy field theories.

Classical BV formalism for group actions (2021)
Journal Article
Benini, M., Safronov, P., & Schenkel, A. (2023). Classical BV formalism for group actions. Communications in Contemporary Mathematics, 25(1), Article 2150094. https://doi.org/10.1142/S0219199721500942

We study the derived critical locus of a function f: [X/G] → 1 on the quotient stack of a smooth affine scheme X by the action of a smooth affine group scheme G. It is shown that dCrit(f) R [Z/G] is a derived quotient stack for a derived affine schem... Read More about Classical BV formalism for group actions.

Categorification of algebraic quantum field theories (2021)
Journal Article
Benini, M., Perin, M., Schenkel, A., & Woike, L. (2021). Categorification of algebraic quantum field theories. Letters in Mathematical Physics, 111(2), Article 35. https://doi.org/10.1007/s11005-021-01371-8

This paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the 2-category... Read More about Categorification of algebraic quantum field theories.

Dirac operators on noncommutative hypersurfaces (2020)
Journal Article
Nguyen, H., & Schenkel, A. (2020). Dirac operators on noncommutative hypersurfaces. Journal of Geometry and Physics, 158, Article 103917. https://doi.org/10.1016/j.geomphys.2020.103917

© 2020 Elsevier B.V. This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures f... Read More about Dirac operators on noncommutative hypersurfaces.

Operads for algebraic quantum field theory (2020)
Journal Article
Benini, M., Schenkel, A., & Woike, L. (2021). Operads for algebraic quantum field theory. Communications in Contemporary Mathematics, 23(2), Article 2050007. https://doi.org/10.1142/S0219199720500078

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 objects provide the operad colors, equipped with an addit... Read More about Operads for algebraic quantum field theory.

On the relationship between classical and deformed Hopf fibrations (2020)
Journal Article
Brzezi?ski, T., Gaunt, J., & Schenkel, A. (2020). On the relationship between classical and deformed Hopf fibrations. Symmetry, Integrability and Geometry: Methods and Applications, 16, https://doi.org/10.3842/sigma.2020.008

The ?-deformed Hopf fibration S3??S2 over the commutative 2-sphere is compared with its classical counterpart. It is shown that there exists a natural isomorphism between the corresponding associated module functors and that the affine spaces of clas... Read More about On the relationship between classical and deformed Hopf fibrations.

Homological perspective on edge modes in linear Yang–Mills and Chern–Simons theory (2020)
Journal Article
Mathieu, P., Murray, L., Schenkel, A., & Teh, N. J. (2020). Homological perspective on edge modes in linear Yang–Mills and Chern–Simons theory. Letters in Mathematical Physics, 110, 1559–1584. https://doi.org/10.1007/s11005-020-01269-x

We provide an elegant homological construction of the extended phase space for linear Yang-Mills theory on an oriented and time-oriented Lorentzian manifold M with a time-like boundary @M that was proposed by Donnelly and Freidel [JHEP 1609, 102 (201... Read More about Homological perspective on edge modes in linear Yang–Mills and Chern–Simons theory.

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.

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.

Locally Covariant Quantum Field Theory with External Sources (2014)
Journal Article
Fewster, C. J., & Schenkel, A. (2015). Locally Covariant Quantum Field Theory with External Sources. Annales Henri Poincaré, 16(10), 2303-2365. https://doi.org/10.1007/s00023-014-0372-y

© 2014, Springer Basel. We provide a detailed analysis of the classical and quantized theory of a multiplet of inhomogeneous Klein–Gordon fields, which couple to the spacetime metric and also to an external source term; thus the solutions form an aff... Read More about Locally Covariant Quantum Field Theory with External Sources.

A C ? -algebra for quantized principal U(1)-connections on globally hyperbolic lorentzian manifolds (2014)
Journal Article
Benini, M., Dappiaggi, C., Hack, T. P., & Schenkel, A. (2014). A C ? -algebra for quantized principal U(1)-connections on globally hyperbolic lorentzian manifolds. Communications in Mathematical Physics, 332(1), 477-504. https://doi.org/10.1007/s00220-014-2100-3

© Springer-Verlag Berlin Heidelberg 2014. The aim of this work is to complete our program on the quantization of connections on arbitrary principal U(1)-bundles over globally hyperbolic Lorentzian manifolds. In particular, we show that one can assig... Read More about A C ? -algebra for quantized principal U(1)-connections on globally hyperbolic lorentzian manifolds.

Quantized Abelian principal connections on Lorentzian manifolds (2014)
Journal Article
Benini, M., Dappiaggi, C., & Schenkel, A. (2014). Quantized Abelian principal connections on Lorentzian manifolds. Communications in Mathematical Physics, 330(1), 123–152. https://doi.org/10.1007/s00220-014-1917-0

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 within an appropriate differential geometric setting... Read More about Quantized Abelian principal connections on Lorentzian manifolds.

Dirac Operators on Noncommutative Curved Spacetimes (2013)
Journal Article
Schenkel, A., & F. Uhlemann, C. (2013). Dirac Operators on Noncommutative Curved Spacetimes. Symmetry, Integrability and Geometry: Methods and Applications, 9, https://doi.org/10.3842/SIGMA.2013.080

We study the notion of a Dirac operator in the framework of twist-deformed noncommutative geometry. We provide a number of well-motivated candidate constructions and propose a minimal set of axioms that a noncommutative Dirac operator should satisfy.... Read More about Dirac Operators on Noncommutative Curved Spacetimes.

Module parallel transports in fuzzy gauge theory (2013)
Journal Article
Schenkel, A. (2014). Module parallel transports in fuzzy gauge theory. International Journal of Geometric Methods in Modern Physics, 11(03), Article 1450021. https://doi.org/10.1142/S0219887814500212

In this paper, we define and investigate a notion of parallel transport on finite projective modules over finite matrix algebras. Given a derivation-based differential calculus on the algebra and a connection on the module, we construct for every der... Read More about Module parallel transports in fuzzy gauge theory.

Linear bosonic and fermionic quantum gauge theories on curved spacetimes (2013)
Journal Article
Hack, T., & Schenkel, A. (2013). Linear bosonic and fermionic quantum gauge theories on curved spacetimes. General Relativity and Gravitation, 45(5), 877-910. https://doi.org/10.1007/s10714-013-1508-y

We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit into this fra... Read More about Linear bosonic and fermionic quantum gauge theories on curved spacetimes.

Quantum Field Theory on Affine Bundles (2013)
Journal Article
Benini, M., Dappiaggi, C., & Schenkel, A. (2014). Quantum Field Theory on Affine Bundles. Annales Henri Poincaré, 15(1), 171-211. https://doi.org/10.1007/s00023-013-0234-z

We develop a general framework for the quantization of bosonic and fermionic field theories on affine bundles over arbitrary globally hyperbolic spacetimes. All concepts and results are formulated using the language of category theory, which allows u... Read More about Quantum Field Theory on Affine Bundles.

Twist deformations of module homomorphisms and connections (2012)
Journal Article
Schenkel, A. (2012). Twist deformations of module homomorphisms and connections. Proceedings of Science, 155, https://doi.org/10.22323/1.155.0056

Let H be a Hopf algebra, A a left H-module algebra and V a left H-module A-bimodule. We study the behavior of the right A-linear endomorphisms of V under twist deformation. We in particular construct a bijective quantization map to the right A_\star-... Read More about Twist deformations of module homomorphisms and connections.

Quantization of the massive gravitino on FRW spacetimes (2012)
Journal Article
Schenkel, A., & F. Uhlemann, C. (2012). Quantization of the massive gravitino on FRW spacetimes. Physical Review D - Particles, Fields, Gravitation and Cosmology, 85(2), https://doi.org/10.1103/PhysRevD.85.024011

In this article we study the quantization and causal properties of a massive spin 3/2 Rarita-Schwinger field on spatially flat Friedmann-Robertson-Walker (FRW) spacetimes. We construct Zuckerman's universal conserved current and prove that it leads t... Read More about Quantization of the massive gravitino on FRW spacetimes.

Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes (2011)
Thesis
Schenkel, A. Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes. (Thesis). Retrieved from https://nottingham-repository.worktribe.com/output/2460579

The focus of this PhD thesis is on applications, new developments and extensions of the noncommutative gravity theory proposed by Julius Wess and his group. In part one we propose an extension of the usual symmetry reduction procedure to noncommut... Read More about Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes.

QFT on homothetic Killing twist deformed curved spacetimes (2011)
Journal Article
Schenkel, A. (2011). QFT on homothetic Killing twist deformed curved spacetimes. General Relativity and Gravitation, 43, 2605–2630. https://doi.org/10.1007/s10714-011-1184-8

We study the quantum field theory (QFT) of a free, real, massless and curvature coupled scalar field on self-similar symmetric spacetimes, which are deformed by an abelian Drinfel'd twist constructed from a Killing and a homothetic Killing vector fie... Read More about QFT on homothetic Killing twist deformed curved spacetimes.

Quantum Field Theory on Curved Noncommutative Spacetimes (2011)
Journal Article
Schenkel, A. (2011). Quantum Field Theory on Curved Noncommutative Spacetimes. Proceedings of Science, 127, https://doi.org/10.22323/1.127.0029

We summarize our recently proposed approach to quantum field theory on noncommutative curved spacetimes. We make use of the Drinfel'd twist deformed differential geometry of Julius Wess and his group in order to define an action functional for a real... Read More about Quantum Field Theory on Curved Noncommutative Spacetimes.

High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing (2010)
Journal Article
Schenkel, A., & F. Uhlemann, C. (2010). High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing. Physics Letters B, 694(3), 258-260. https://doi.org/10.1016/j.physletb.2010.09.066

We consider an interacting scalar quantum field theory on noncommutative Euclidean space. We implement a family of noncommutative deformations, which -- in contrast to the well known Moyal-Weyl deformation -- lead to a theory with modified kinetic te... Read More about High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing.

Field Theory on Curved Noncommutative Spacetimes (2010)
Journal Article
Schenkel, A., & F. Uhlemann, C. (2010). Field Theory on Curved Noncommutative Spacetimes. Symmetry, Integrability and Geometry: Methods and Applications, 6, Article 061. https://doi.org/10.3842/SIGMA.2010.061

We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005), 3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative spacetimes by us... Read More about Field Theory on Curved Noncommutative Spacetimes.

Spacetime Noncommutativity in Models with Warped Extradimensions (2010)
Journal Article
Ohl, T., Schenkel, A., & F. Uhlemann, C. (2010). Spacetime Noncommutativity in Models with Warped Extradimensions. Journal of High Energy Physics, Article 29. https://doi.org/10.1007/JHEP07%282010%29029

We construct consistent noncommutative (NC) deformations of the Randall-Sundrum spacetime that solve the NC Einstein equations with a non-trivial Poisson tensor depending on the fifth coordinate. In a class of these deformations where the Poisson ten... Read More about Spacetime Noncommutativity in Models with Warped Extradimensions.

Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes (2010)
Journal Article
Ohl, T., & Schenkel, A. (2010). Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes. General Relativity and Gravitation, 42(12), 2785–2798. https://doi.org/10.1007/s10714-010-1016-2

In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel'd twists. We construct deformed quadratic action functionals and compu... Read More about Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes.

Preferred foliation effects in Quantum General Relativity (2010)
Journal Article
Koslowski, T., & Schenkel, A. (2010). Preferred foliation effects in Quantum General Relativity. Classical and Quantum Gravity, 27(13), Article 135014. https://doi.org/10.1088/0264-9381/27/13/135014

We investigate the infrared (IR) effects of Lorentz violating terms in the gravitational sector using functional renormalization group methods similar to Reuter and collaborators. The model we consider consists of pure quantum gravity coupled to a pr... Read More about Preferred foliation effects in Quantum General Relativity.

Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity (2009)
Journal Article
Ohl, T., & Schenkel, A. (2009). Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity. Journal of High Energy Physics, 2009, https://doi.org/10.1088/1126-6708/2009/10/052

We derive noncommutative Einstein equations for abelian twists and their solutions in consistently symmetry reduced sectors, corresponding to twisted FRW cosmology and Schwarzschild black holes. While some of these solutions must be rejected as model... Read More about Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity.

Symmetry Reduction and Exact Solutions in Twisted Noncommutative Gravity (2009)
Journal Article
Schenkel, A. (2009). Symmetry Reduction and Exact Solutions in Twisted Noncommutative Gravity. Acta Physica Polonica B Proceedings Supplement, 2(3), 657-667

We review the noncommutative gravity of Wess et al. and discuss its physical applications. We define noncommutative symmetry reduction and construct deformed symmetric solutions of the noncommutative Einstein equations. We apply our framework to find... Read More about Symmetry Reduction and Exact Solutions in Twisted Noncommutative Gravity.

Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes (2009)
Journal Article
Ohl, T., & Schenkel, A. (2009). Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes. Journal of High Energy Physics, 2009, Article JHEP01(2009)084. https://doi.org/10.1088/1126-6708/2009/01/084

As a preparation for a mathematically consistent study of the physics of symmetric spacetimes in a noncommutative setting, we study symmetry reductions in deformed gravity. We focus on deformations that are given by a twist of a Lie algebra acting on... Read More about Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes.