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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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Contributor : Nicolas Gilliers <>
Submitted on : Sunday, April 28, 2019 - 2:54:13 PM
Last modification on : Friday, March 27, 2020 - 3:53:59 AM


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  • HAL Id : hal-02113282, version 1


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



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