Kinks in the Hartree approximation

Abstract

The topological defects of $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ theory, the kink and antikink, are studied in the Hartree approximation. This allows us to discuss quantum effects on defects in both stationary and dynamical systems. The kink mass is calculated for a number of parameters, and compared to classical, one loop and Monte Carlo results known from the literature. We discuss the thermalization of the system after a kink-antikink collision. A classical result, the existence of a critical speed, is rederived and shown for the first time in quantum theory. We also use kink-antikink collisions as a very simple toy model for heavy ion collisions and discuss the differences and similarities, for example, in pressure. Finally, using the Hartree ensemble approximation allows us to study kink-antikink nucleation starting from a thermal (Bose--Einstein) distribution. On a qualitative level, our results show only few dissimilarities with the classical results, but on a quantitative level there are some important differences.