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Metaplectic spinor fields and global anomalies

Technical Report:

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.)
Authors:
Publication Date:
Sep 01, 1994
Product Type:
Technical Report
Report Number:
DESY-94-157
Reference Number:
SCA: 662110; PA: DEN-94:0FO475; EDB-95:025617; SN: 95001313536
Resource Relation:
Other Information: PBD: Sep 1994
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; SIGMA MODEL; SPINOR FIELDS; PHASE SPACE; FERMIONS; FEYNMAN PATH INTEGRAL; HAMILTONIANS; IRREDUCIBLE REPRESENTATIONS; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; PARTITION FUNCTIONS; SP GROUPS; CURRENT DIVERGENCES; TOPOLOGICAL MAPPING; LAGRANGIAN FIELD THEORY; WAVE FUNCTIONS; CREATION OPERATORS; ANNIHILATION OPERATORS; ANALYTIC FUNCTIONS; SMOOTH MANIFOLDS; TOPOLOGY; 662110; THEORY OF FIELDS AND STRINGS
OSTI ID:
10107974
Research Organizations:
Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
Journal ID: ISSN 0418-9833; Other: ON: DE95731949; TRN: DE94FO475
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
DEN
Size:
29 p.
Announcement Date:
Jun 30, 2005

Technical Report:

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}
}