Vacuum polarization in a nonsimply connected spacetime

Journal Article · Fri Feb 15 04:00:00 EST 1980 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.21.933· OSTI ID:5660451

Ford, L H

The vacuum polarization tensor of spinor electrodynamics is calculated to order e/sup 2/ in a nonsimply connected spacetime with the topology of S/sup 1/ x R/sup 3/, flat spacetime with periodicity in one spatial dimension. In contrast to the situation in a simply connected spacetime, there are two distinct types of spinors in this spacetime, the untwisted spinors and the twisted spinors. The vacuum polarization due to each type of spinor is calculated; it is found that the two types of spinors give rise to different vacuum polarization effects and hence must be regarded as physically inequivalent. The effect of the vacuum polarization upon photon propagation is considered, and it is shown that untwisted spinors give rise to noncausal effects whereas twisted spinors do not. The vacuum energy for a free spinor field in S/sup 1/ x R/sup 3/ is also calculated, and it is found that the twisted configuration gives rise to a vacuum state of lower energy than does the untwisted configuration. Various methods of incorporating twisted and untwisted spinors into the same theory, either as distinct fields or as different sectors of the same field theory, are discussed. No tractable method of incorporating both types of spinors is found which avoids the difficulty of noncausal photon propagation. It is therefore proposed that only the twisted spinors should be regarded as having physical significance.

• Research Organization: Department of Mathematics, University of London, King's College, London WC2R 2LS, United Kingdom
• OSTI ID: 5660451
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 21:4; ISSN PRVDA
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY CONDITIONS
ELECTRODYNAMICS
ELEMENTARY PARTICLES
FIELD THEORIES
MASSLESS PARTICLES
MATHEMATICAL SPACE
MINKOWSKI SPACE
PHOTONS
QUANTUM FIELD THEORY
RENORMALIZATION
SPACE
SPACE-TIME
SPINORS
VACUUM POLARIZATION
VACUUM STATES