Collective Coordinate Quantization: Relativistic and Gauge Symmetric Aspects

TL;DR

This paper develops a gauge-invariant, relativistic approach to quantizing the center-of-mass coordinate of solitons in (1+1)D nonlinear field theories, highlighting gauge and BRST-symmetry aspects and analyzing soliton dynamics.

Contribution

It introduces a novel gauge-independent method for collective coordinate quantization that incorporates Lorentz invariance and retardation effects for solitons.

Findings

Retardation effects alter quantum mechanics of extended solitons.

A gauge and BRST-symmetric framework for collective coordinates is established.

Effective soliton-meson interactions are analyzed, showing acceleration and internal excitation.

Abstract

The introduction and quantization of a center-of-mass coordinate is demonstrated for the one-soliton sector of nonlinear field theories in (1+1) dimensions. The present approach strongly emphazises the gauge and BRST-symmetry aspects of collective coordinate quantization. A gauge is presented which is independent of any approximation scheme and which allows to interpret the new degree of freedom as the {\em quantized} center of mass coordinate of a soliton. Lorentz invariance is used from the beginning to introduce fluctuations of the collective coordinate in the {\em rest frame} of the {\em moving} soliton. It turns out that due to the extended nature of the soliton retardation effects lead to differences in the quantum mechanics of the soliton as compared to a point-like particle. Finally, the results of the semiclassical expansion are used to analyse effective soliton-meson vertices and the coupling to an external source. Such a coupling in general causes acceleration as well as internal excitation of the soliton.