Quantum Mechanics on Moduli Spaces

TL;DR

This paper examines the validity and details of approximating quantum BPS soliton interactions via moduli space quantization, highlighting new geometrical and dynamical terms, especially in supersymmetric models.

Contribution

It provides a detailed analysis of the Born-Oppenheimer approximation in quantum systems on moduli spaces, including new terms and their geometric and dynamical origins, with extensions to supersymmetric sigma models.

Findings

New geometrical and dynamical terms identified in the reduction process.

Most extra terms vanish in supersymmetric sigma models.

General properties of quantum reduction via Born-Oppenheimer approximation analyzed.

Abstract

It has been assumed that it is possible to approximate the interactions of quantized BPS solitons by quantising a dynamical system induced on a moduli space of soliton parameters. General properties of the reduction of quantum systems by a Born-Oppenheimer approximation are described here and applied to sigma models and their moduli spaces in order to learn more about this approximation. New terms arise from the reduction proceedure, some of them geometrical and some of them dynamical in nature. The results are generalised to supersymmetric sigma models, where most of the extra terms vanish.