2020/05/25 by Gilliers, Nicolas
#46L54 #57T05 #60J65 #81T13 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
paper · doi:10.48550/arxiv.2005.12029
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.