INVESTIGATION OF A THEORY WITH SOLITON-LIKE CONFIGURATIONS

Motivated by the study of classical finite-action field configurations of higher order Yang-Mills-Higgs theories, we construct the Lagrangian of a scalar theory in one space and one time dimensions which can serve as a relatively simple model for the investigation of the properties of theories with finite energy or action classical configurations. The condition of stability of the classical configuration, the zero mode and the significance of the latter in connection with constraints which ensure the existence of the Green’s function, are studied in detail. It is then shown how a Schrödinger equation can be established and solved whose eigenfunctionals determine the probability of field fluctuations in the neighborhood of the classical configuration.