Excited Kinks as Quantum States

TL;DR

This paper calculates the first correction beyond one loop to the quantum states of excited kinks, providing new insights into their energy spectrum and developing a diagrammatic method for such quantum field theory calculations.

Contribution

It introduces the first correction beyond one loop for excited kink states and proposes a diagrammatic approach for these quantum corrections.

Findings

First correction beyond one loop for excited kink states.

Two-loop correction to the energy of excited normal modes.

Relation of unbound mode correction to nonrelativistic kinetic energy and one-loop mass correction.

Abstract

At one loop, quantum kinks are described by a sum of quantum harmonic oscillator Hamiltonians, and so their spectra are known exactly. We find the first correction beyond one loop to the quantum states corresponding to kinks with an excited bound or unbound normal mode, and also the corresponding two-loop correction to the energy cost of exciting the normal mode. In the case of unbound normal modes, this correction is equal to sum of the corresponding nonrelativistic kinetic energy plus the usual one-loop correction to the mass of the corresponding plane wave in the absence of a kink. We also sketch a diagrammatic method for such calculations.