# Equivariant Metaplectic-c Prequantization of Symplectic Manifolds with Hamiltonian Torus Actions

## TL;DR

This paper establishes a necessary and sufficient condition for a symplectic manifold with a Hamiltonian torus action to admit an equivariant metaplectic-c prequantization, and applies it to identify quantized energy levels.

## Contribution

It generalizes the condition for equivariant metaplectic-c prequantization to symplectic manifolds with torus actions and relates it to quantized energy levels.

## Key findings

- Derived a condition evaluated at fixed points of the momentum map.
- Extended previous energy quantization conditions to torus actions.
- Provided criteria for the existence of equivariant metaplectic-c prequantizations.

## Abstract

This paper determines a condition that is necessary and sufficient for a metaplectic-c prequantizable symplectic manifold with an effective Hamiltonian torus action to admit an equivariant metaplectic-c prequantization. The condition is evaluated at a fixed point of the momentum map, and is shifted from the one that is known for equivariant prequantization line bundles. Given a metaplectic-c prequantized symplectic manifold with a Hamiltonian energy function, the author previously proposed a condition under which a regular value of the function should be considered a quantized energy level of the system. This definition naturally generalizes to regular values of the momentum map for a Hamiltonian torus action. We state the generalized definition for such a system, and use an equivariant metaplectic-c prequantization to determine its quantized energy levels.