An Extended Soliton's Zero Modes

TL;DR

This paper investigates the quantum properties of extended solitons like domain walls and membranes, focusing on their zero modes, and calculates the probability of exciting their translation modes by incoming radiation.

Contribution

It explicitly constructs quantum states for extended solitons considering zero modes, extending previous work on localized solitons to higher-dimensional structures.

Findings

Constructed quantum states for domain walls and membranes with zero modes.

Calculated excitation probabilities for soliton translation modes.

Analyzed both compact and infinitely extended solitons.

Abstract

Quantum field theory in the presence of localized solitons is more complicated than vacuum sector quantum field theory, largely as a result of the soliton's zero modes. In the present work, we try to understand to what extent this situation carries over to extended solitons. To this end, we explicitly construct the quantum state corresponding to a domain wall string or membrane, treating the zero modes carefully. This is done both for compact and also infinitely extended solitons. As an application, we calculate the differential probability for a domain wall string's translation mode, with a given momentum, to be excited by a single quantum of incoming radiation.