Quantum Holonomy Fields

Abstract

We investigate lattice and continuous quantum gauge theories on the Euclidean plane with a structure group that is replaced by a $H$-algebra; 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 Quantum Holonomy Hield over a $H$-algebra and construct such fields starting from a quantum Lévy process on a $H$-algebra. As an application, we define higher-dimensional generalizations of the so-called master field.

References in corpus (5)

• Three proofs of the Makeenko-Migdal equation for Yang-Mills theory on the plane
• Hopf algebra gauge theory on a ribbon graph
• The generalized master fields
• The Theory of Quantum Levy Processes
• Matricial approximations of higher dimensional master fields

Cited by in corpus (1)

• Matricial approximations of higher dimensional master fields