Quantum Holonomy on a Lattice
Journal
Modern Physics Letters A
Journal Volume
8
Journal Issue
31
Pages
2911-2918
Date Issued
1993
Author(s)
Lee, Hc
Abstract
The quantum holonomy associated with a set of contours on a lattice is shown to be a Casimir operator of the gauge group. Its value in an irreducible representation of the group is the unit matrix times a c-number. This assertion is verified numerically on a 4D lattice for the SU(3) pure gauge theory for cases of the set containing one and two contours. The group-valued quantum holonomy contains more useful information than the character-valued Wilson loop in aspects that could be crucial. The quantum holonomy of a set of loops could serve as an observable for measuring the correlations between the gauge loops.
Type
journal article