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. (orig.)
Citation Formats
Reuter, M.
Metaplectic spinor fields and global anomalies.
Germany: N. p.,
1994.
Web.
Reuter, M.
Metaplectic spinor fields and global anomalies.
Germany.
Reuter, M.
1994.
"Metaplectic spinor fields and global anomalies."
Germany.
@misc{etde_10107974,
title = {Metaplectic spinor fields and global anomalies}
author = {Reuter, M}
abstractNote = {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. (orig.)}
place = {Germany}
year = {1994}
month = {Sep}
}
title = {Metaplectic spinor fields and global anomalies}
author = {Reuter, M}
abstractNote = {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. (orig.)}
place = {Germany}
year = {1994}
month = {Sep}
}