Anyonic states in Chern-Simons theory

Journal Article · Thu Dec 15 00:00:00 EST 1994 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.50.7519· OSTI ID:7058567

Haller, K; Lim-Lombridas, E ^[1]

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1. Department of Physics, University of Connecticut, Storrs, Connecticut 06269 (United States)

We discuss the canonical quantization of Chern-Simons theory in 2+1 dimensions, minimally coupled to a Dirac spinor field, first in the temporal gauge and then in the Coulomb gauge. In our temporal gauge formulation, Gauss's law and the gauge condition [ital A][sub 0]=0 are implemented by embedding the formulation in an appropriate physical subspace. We construct a Fock space of charged particle states that satisfy Gauss's law, and show that they obey fermion, not fractional statistics. The gauge-invariant spinor field that creates these charged states from the vacuum obeys the anticommutation rules that generally apply to spinor fields. The Hamiltonian, when described in the representation in which the charged fermions are the propagating particle excitations that obey Gauss's law, contains an interaction between charge and transverse current densities. We observe that the implementation of Gauss's law and the gauge condition does not require us to use fields with graded commutator algebras or particle excitations with fractional statistics. In our Coulomb gauge formulation, we implement Gauss's law and the gauge condition [partial derivative][sub [ital l]][ital A][sub [ital l]]=0 by the Dirac-Bergmann procedure. In this formulation, the constrained gauge fields become functionals of the spinor fields, and are not independent degrees of freedom. The formulation in the Coulomb gauge confirms the results we obtained in the temporal gauge: The Dirac-Bergmann'' anticommutation rule for the charged spinor fiels [psi] and [psi][sup [degree]] that have both been constrained to obey Gauss's law is precisely identical to the canonical spinor anticommutation rule that generates standard fermion statistics. And we also show that the Hamiltonians for charged particle states in our temporal and Coulomb gauge formulations are identical, once Gauss's law has been implemented in both cases.

• DOE Contract Number: FG02-92ER40716
• OSTI ID: 7058567
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 50:12; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
UNIFIED GAUGE MODELS
ANYONS
QUANTIZATION
CHARGED PARTICLES
COMMUTATION RELATIONS
DEGREES OF FREEDOM
EXCITATION
FOCK REPRESENTATION
GAUGE INVARIANCE
HAMILTONIANS
MAXWELL EQUATIONS
SPINOR FIELDS
STATISTICS
THREE-DIMENSIONAL CALCULATIONS
VACUUM STATES
DIFFERENTIAL EQUATIONS
ENERGY-LEVEL TRANSITIONS
EQUATIONS
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
QUANTUM OPERATORS
QUASI PARTICLES
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)
661100 - Classical & Quantum Mechanics- (1992-)