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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.