All Outputs (64)

Supergeometry in locally covariant quantum field theory (2015)
Journal Article
Hack, T.-P., 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. https://doi.org/10.4310/atmp.2014.v18.n3.a1

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.-P., & 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)
Presentation / Conference Contribution
Schenkel, A. Twist deformations of module homomorphisms and connections. Presented at Corfu Summer Institute 2011, Corfu, Greece

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), Article 024011. 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). 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.