Dirac versus Reduced Quantization of the Poincaré Symmetry in Scalar Electrodynamics

Details Dirac versus Reduced Quantization of the Poincaré Symmetry in Scalar Electrodynamics Dirac versus Reduced Quantization of the Poincaré Symmetry in Scalar Electrodynamics

1994-03-31

arxiv.org/abs/gr-qc/9403065v1

Phys.Rev. D51 (1995) 781-799

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages

Scientific paper

10.1103/PhysRevD.51.781

The generators of the Poincar\'{e} symmetry of scalar electrodynamics are quantized in the functional Schr\"{o}dinger representation. We show that the factor ordering which corresponds to (minimal) Dirac quantization preserves the Poincar\'{e} algebra, but (minimal) reduced quantization does not. In the latter, there is a van Hove anomaly in the boost-boost commutator, which we evaluate explicitly to lowest order in a heat kernel 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.

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