2 research outputs found
Dirac versus Reduced Quantization of the Poincar\'{e} Symmetry in Scalar Electrodynamics
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.Comment: 24 page