Equivariant prequantization and the moment map

TL;DR

This paper establishes criteria for equivariant pre-quantization of closed G-invariant 2-forms with moment maps, providing explicit obstruction calculations for lifting group actions to pre-quantization bundles for compact, connected Lie groups.

Contribution

It offers necessary and sufficient conditions for equivariant pre-quantizability based on the moment map, and computes obstructions to lifting group actions to pre-quantization bundles.

Findings

Derived conditions for equivariant pre-quantization

Computed obstructions to lifting G-actions

Applicable to any compact, connected Lie group

Abstract

If {\omega} is a closed G-invariant 2-form and {\mu} a moment map, then we obtain necessary and sufficient conditions for equivariant pre-quantizability that can be computed in terms of the moment map {\mu}. We also compute the obstructions to lift the action of G to a pre-quantization bundle of {\omega}. Our results are valid for any compact and connected Lie group G.