Quasi-coherent states for unitary groups

Abstract

The author extends a recent construction of isotropic spin-coherent states to unitary groups. Expectation values in such a quasi-coherent state can be obtained from a generating functional which is given explicitly for the fundamental and the adjoint representations of the unitary groups SU(N) and U(N). The close connection between the corresponding generating functional and the external field problem in QCD is pointed out. Free quantum fields in such a condensed, colour singlet, coherent state are formally related to two-dimensional lattice gauge theories with, in general, a mixed action. In the large-N limit, the author exhibits a phase transition for a free quantum field in a singlet quasi-coherent state. A path integral representation of the transition amplitude in terms of quasi-coherent states is also given. The corresponding effective action describes dynamics on a complex Kahler manifold.