Dirac versus reduced quantization of the Poincare symmetry in scalar electrodynamics

Journal Article · Sun Jan 15 04:00:00 EST 1995 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.51.781· OSTI ID:6604919

Epp, R J ^[1]; Kunstatter, G ^[2]

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1. Physics Department, University of Winnipeg, Winnipeg, Manitoba, R3B 2E9 (Canada)
2. Physics Department, University of Manitoba, Winnipeg, Manitoba, R3T 2N2 (Canada) Winnipeg Institute for Theoretical Physics, Physics Department, University of Winnipeg, Winnipeg, Manitoba, R3B 2E9 (Canada)

The generators of the Poincare symmetry of scalar electrodynamics are quantized in the functional Schroedinger representation. We show that the factor ordering which corresponds to (minimal) Dirac quantization preserves the Poincare algebra, but (minimal) reduced quantization does not. In the latter, there is a van Hove anomaly in the boost-boost commmutator, which we evaluate explicitly to lowest order in a heat kernal expansion using [zeta]-function regularization. We illuminate the crucial role played by the gauge orbit volume element in the analysis. Our results demonstrate that preservation of extra symmetries at the quantum level is sometimes a useful criterion to select between inequivalent, but nevertheless self-consistent, quantization schemes.

• OSTI ID: 6604919
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 51:2; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

661100 -- Classical & Quantum Mechanics-- (1992-)
662110 -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
662120* -- General Theory of Particles & Fields-- Symmetry
Conservation Laws
Currents & Their Properties-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ELECTRODYNAMICS
FIELD THEORIES
LIE GROUPS
POINCARE GROUPS
QUANTIZATION
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
SCALAR FIELDS
SCHROEDINGER PICTURE
SYMMETRY GROUPS