Topological defects as inhomogeneous condensates in Quantum Field Theory: Kinks in (1+1) dimensional $\la \psi^4$ theory

TL;DR

This paper develops a quantum field theoretical approach to topological defects, specifically kinks in a (1+1)D $ ext{λ} ext{ψ}^4$ model, demonstrating how classical solutions emerge from quantum operators and extending the method to finite temperature and non-equilibrium scenarios.

Contribution

It introduces a general method to derive classical topological defect solutions from quantum operators within the Closed-Time-Path formalism, applicable at finite temperature and out of equilibrium.

Findings

Classical kink solutions derived from quantum vacuum expectation values.

Method applicable to finite temperature and non-equilibrium conditions.

Discussion on high-temperature behavior of kinks.

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 $\la \psi^4$ model and construct the Heisenberg picture field operator $\psi$ 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.