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

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.