Quantum Holonomy Fields
Mathematical Physics
2023-03-31 v4 math.MP
Probability
Abstract
We investigate lattice and continuous quantum gauge theories on the Euclidean plane with a structure group that is replaced by a -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 -algebra and construct such fields starting from a quantum L\'evy process on a -algebra. As an application, we define higher-dimensional generalizations of the so-called master field.
Cite
@article{arxiv.2005.12029,
title = {Quantum Holonomy Fields},
author = {Nicolas Gilliers},
journal= {arXiv preprint arXiv:2005.12029},
year = {2023}
}