Operator ordering problem of the nonrelativistic Chern-Simons theory
- Department of Physics and Basic Science Research Institute, Sogang University, C.P.O. Box 1142, Seoul 100-611 (Korea, Republic of)
The operator ordering problem due to the quantization or regularization ambiguity in the Chern-Simons theory exists. However, we show that this can be avoided if we require Galilei covariance of the nonrelativistic Abelian Chern-Simons theory even at the quantum level for the extended sources. The covariance can be recovered only by choosing some particular operator orderings for the generators of the Galilei group depending on the quantization ambiguities of the gauge-matter commutation relation. We show that the desired ordering for the unusual prescription is not the same as the well-known normal ordering but still satisfies all the necessary conditions. Furthermore we show that the equations of motion can be expressed in a similar form regardles of the regularization ambiguity. This suggests that the different regularization prescriptions do not change the physics. On the other hand, for the case of point sources the regularization prescription is uniquely determined, and only the orderings, which are equivalent to the usual one, are allowed.
- OSTI ID:
- 6818570
- Journal Information:
- Physical Review, D (Particles Fields); (United States), Vol. 50:12; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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COMPOSITE MODELS
QUANTUM OPERATORS
COMMUTATION RELATIONS
UNIFIED GAUGE MODELS
ANYONS
CONFINEMENT
EQUATIONS OF MOTION
GALILEI TRANSFORMATIONS
QUANTIZATION
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
QUASI PARTICLES
TRANSFORMATIONS
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