Batalin-Vilkovisky field-antifield quantisation of fluctuations around classical field configurations

TL;DR

This paper applies the Batalin-Vilkovisky formalism to soliton quantisation, clarifying the role of zero modes, collective coordinates, and gauge invariance, with an application to the nonlinear O(3) sigma-model.

Contribution

It introduces a BV-based method for quantising fluctuations around classical solitons, emphasizing the canonical transformation and gauge symmetry aspects.

Findings

Clarifies the relation between zero modes and gauge invariance.

Shows how to separate quantum fluctuations from collective motion.

Applies the method to the nonlinear O(3) sigma-model.

Abstract

The Lagrangian field-antifield formalism of Batalin and Vilkovisky (BV) is used to investigate the application of the collective coordinate method to soliton quantisation. It is shown how Noether identities and local symmetries of the Lagrangian arise when collective coordinates are introduced in order to avoid divergences related to zero modes. This transformation to collective and fluctuation degrees of freedom is interpreted as a canonical transformation in the symplectic field-antifield space which induces a time-local gauge symmetry. Separating the corresponding Lagrangian path integral of the BV scheme in lowest order into harmonic quantum fluctuations and a free motion of the collective coordinate with the classical mass of the soliton, we show how the BV approach clarifies the relation between zero modes, collective coordinates, gauge invariance and the center-of-mass motion of classical solutions in quantum fields. Finally, we apply the procedure to the reduced nonlinear O(3) sigma-model.