QUANTUM HOLONOMY ON A LATTICE

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 ir reducible representation of the group is the unit matrix times a c-num ber. 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 cont ours. The group-valued quantum holonomy contains more useful informati on than the character-valued Wilson loop in aspects that could be cruc ial. The quantum holonomy of a set of loops could serve as an observab le for measuring the correlations between the gauge loops.