Covariant method for soliton matrix elements.

Abstract

We construct field-theory wave functions for soliton and other collective states in field theory. The formalism is covariant, incorporates zero modes, and the states can be directly related to states postulated in the standard Hamiltonian quantization procedures. By explicitly constructing the states using a generalized coherent-state expansion, we present the calculation of matrix elements of functions of operators in a general linearization scheme and reduce such calculations to ordinary functions of classical fields. The results include the dependence of matrix elements on a regularization scale ${\ensuremath{\mu}}^{2}$, momentum transfer ${q}^{\ensuremath{\mu}}$, the overlap of states having different position indices, and the classical configuration. We construct momentum eigenstates and examine the semiclassical limit \ensuremath{\Elzxh}\ensuremath{\rightarrow}0. Although most of the analysis is expressed in free-field or plane-wave modes for definiteness, the generalization to modes defined by an arbitrary linearization procedure is presented. We also discuss the separation of divergences from zero-point fluctuations versus classical divergences from topological sectors.