METAPLECTIC SPINOR FIELDS AND GLOBAL ANOMALIES

Abstract

We investigate spinor fields on phase spaces. Under local frame rotations they transform according to the (infinite-dimensional, unitary) metaplectic representation of Sp(2N), which plays a role analogous to the Lorentz group. We introduce a one-dimensional nonlinear sigma model whose target space is the phase space under consideration. The global anomalies of this model are analyzed, and it is shown that its fermionic partition function is anomalous exactly if the underlying phase space is not a spin manifold, i.e. if metaplectic spinor fields cannot be introduced consistently. The sigma model is constructed by giving a path integral representation to the Lie transport of spinors along the Hamiltonian flow.