Topological defects as inhomogeneous condensates in Quantum Field Theory: Kinks in (1+1) dimensional $\la ψ^4$ 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 $\la ψ^4$ 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 $\la \to 0$ limit. The presented method is general in the sense that 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 $T\neq 0$ 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.