Geometric Quantization of the moduli space of the vortex equations on a Riemann surface

TL;DR

This paper presents a method for quantizing the symplectic form on the vortex moduli space of a Riemann surface by modifying the Quillen metric, contributing to geometric quantization techniques.

Contribution

It introduces a novel approach to geometric quantization of vortex moduli spaces using a modified Quillen metric on the determinant line bundle.

Findings

Quantization of the vortex moduli space achieved

Modified Quillen metric effectively encodes quantum structure

Provides a new perspective on geometric quantization methods

Abstract

In this note we quantize the usual symplectic (K\"{a}hler) form on the vortex moduli space by modifying the Quillen metric of the Quillen determinant line bundle.