Topological Defects as Inhomogeneous Condensates in Quantum Field Theory: Kinks in (1+1) Dimensional λψ4 Theory

Abstract

We study topological defects as inhomogeneous (localized) condensates of particles in quantum field theory. In the framework of the closed-time-path formalism, we consider explicitly a (1+1) dimensional λψ4 model and construct the Heisenberg picture field operator ψ in the presence of kinks. We show how the classical kink solutions emerge from the vacuum expectation value of such an operator in the Born approximation and/or λ→0 limit. The presented method is general in the sense that it applies also to the case of finite temperature and to non-equilibrium; it also allows for the determination of Green's functions in the presence of topological defects. We discuss the classical kink solutions at T≠0 in the high temperature limit. We conclude with some speculations on the possible relevance of our method for the description of the defect formation during symmetry-breaking phase transitions.