MODELING THE FIELD-THEORY SKYRMION

We consider the Skyrme soliton from the viewpoint of realistic fluctuations about a quantum condensed phase. To study this, a systematic presentation of methods to obtain field-theory matrix elements for the Skyrmion and other extended states is given. The approach concentrates on maintaining covariance, translational invariance and other symmetries in a consistent quantum mechanical framework. The quantum kinematical features of Gaussian fluctuations and resulting matrix elements of local operators do not agree with common replacements such as the large F_π and mean-field prescriptions, but are investigated as a function of momentum transfer, parameters defining the field distributions, and the ultraviolet regulator. We emphasize the need for off-diagonal distribution functions, construct explicit momentum in-states, and illustrate methods of calculation with examples. Much of the presentation is designed to avoid sigma-model formalism, topological arguments etc., in order to highlight the quantum mechanics for students and others learning about solitons.