Non-commutative gauge theories and Zhang algebras

Abstract : We investigate lattice and continuous quantum gauge theories on the Euclidean plane with a structure group that is replaced by a Zhang algebra. Zhang algebras are non-commutative analogues of groups and contain the class of Voiculescu's dual groups. We are interested in non-commutative analogues of random gauge fields, which we describe through the random holonomy that they induce. We propose a general definition of a holonomy field with Zhang gauge symmetry, and construct a such fields starting from a quantum Lévy process on a Zhang algebra. As an application, we define higher dimensional generalizations of the so-called master field.
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https://hal.archives-ouvertes.fr/hal-02113282
Contributor : Nicolas Gilliers <>
Submitted on : Sunday, April 28, 2019 - 2:54:13 PM
Last modification on : Wednesday, May 15, 2019 - 3:45:41 AM

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  • HAL Id : hal-02113282, version 1

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Nicolas Gilliers. Non-commutative gauge theories and Zhang algebras. 2019. ⟨hal-02113282⟩

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