Metastable States in a Field Theory

Abstract

Real scalar -lop' field theory with tachionic mass term is shown to possess translation­ ally non-symmetric c-number field configurations when studied on a lattice space. The field configurations behave as static stable mean fields at finite lattice spacing and become unstable in the continuum limit. Possibility of phase transitions at finite temperature is discussed with the aid of these mean fields where quantum effects are taken into account to lowest order in -l. § I. Introduction One of the most interesting subjects in quantized field theory is to study classi­ cal field configurations which appear through interactions among fields without external sources. 1l If the field configurations are localized in the sense that the field energies are confined in a microscopic region of space, they help us to study field theoretical aspects of hadron structure. The static kink solution in one space dimension 2l is a candidate for such purpose. When the field configurations extend over space macroscopically, they are interpreted as mean fields which specify the gross behavior of the field system just like phases in many-body physics. In the present paper we study metastable classical field configurations confining ourselves to this latter case. We examine a field theory constructed in a lattice space. The successful explanation of the weak and the electromagnetic interaction based on the Weinberg-Salam modePl. 4l has revealed the relevance of broken sym­ metry vacuum with particle physics. The implied vacuum is one of those generated by non-linear interactions among the Higgs scalar fields 5l where a mean field deve­ lops over the space-time as a constant field. The excitation spectra around the vacuum such as quantum Higgs modes and vector mesons of heavy masses await their experimental supports. The mean fields should be the stable e-n umber solutions of field equations. The field configurations are vacuum expectation values of the quantized fields of the system. In general, vacuum does not fully account for the symmetrical proper­ ties of the field equations so that spontaneous breakings of the symmetries take place. Owing to lack of available stable solutions, 6l however, the types of the broken symmetries considered so far are limited to a few. 7l In particular, possible existence of metastable vacua corresponding to translationally inhomogeneous mean fields have not satisfactorily been investigated. The lattice field theory we study