Dressing Up the Kink

TL;DR

This paper constructs a quantum (dressed) kink solution in a scalar field theory using a self-consistent Hartree approximation, revealing quantum effects on the kink's energy, profile, and temperature dependence.

Contribution

It introduces a self-consistent quantum kink solution incorporating quantum fluctuations via the 2PI effective action in the Hartree approximation, including backreaction effects.

Findings

Quantum kink has lower energy than classical but higher than 1-loop results.

Quantum kink exists at finite temperature and broadens with increasing temperature.

Quantum fluctuations lower the fluctuation spectrum in the presence of the defect.

Abstract

Many quantum field theoretical models possess non-trivial solutions which are stable for topological reasons. We construct a self-consistent example for a self-interacting scalar field--the quantum (or dressed) kink--using a two particle irreducible effective action in the Hartree approximation. This new solution includes quantum fluctuations determined self-consistently and nonperturbatively at the 1-loop resummed level and allowed to backreact on the classical mean-field profile. This dressed kink is static under the familiar Hartree equations for the time evolution of quantum fields. Because the quantum fluctuation spectrum is lower lying in the presence of the defect, the quantum kink has a lower rest energy than its classical counterpart. However its energy is higher than well-known strict 1-loop results, where backreaction and fluctuation self-interactions are omitted. We also show that the quantum kink exists at finite temperature and that its profile broadens as temperature is increased until it eventually disappears.