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Noncommutative Field Theories from a Deformation Point of View

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Quantum Field Theory

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Abstract

In this review we discuss the global geometry of noncommutative field theories from a deformation point of view: The space-times under consideration are deformations of classical space-time manifolds using star products. Then matter fields are encoded in deformation quantizations of vector bundles over the classical space-time. For gauge theories we establish a notion of deformation quantization of a principal fibre bundle and show how the deformation of associated vector bundles can be obtained.

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Authors and Affiliations

  1. Fakultät für Mathematik und Physik, Albert-Ludwigs-Universität Freiburg Physikalisches Institut, Hermann Herder Strasse 3, DE-79104, Freiburg

    Stefan Waldmann

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  1. Stefan Waldmann
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  1. Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstrasse 22-26, D-04103, Leipzig, Germany

    Bertfried Fauser , Jürgen Tolksdorf  & Eberhard Zeidler ,  & 

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Waldmann, S. (2009). Noncommutative Field Theories from a Deformation Point of View. In: Fauser, B., Tolksdorf, J., Zeidler, E. (eds) Quantum Field Theory. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8736-5_7

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