Exotic Spin and Statistics in (2+1)-Dimensional Canonical Quantum Field Theory

Semenoff, Gordon W.; Sodano, Pasquale

doi:10.1016/0550-3213(89)90229-0

Exotic Spin and Statistics in (2+1)-Dimensional Canonical Quantum Field Theory

Gordon W. Semenoff
(
- British Columbia U.
)
,
Pasquale Sodano
(
- Los Alamos
)

Mar 21, 1989

24 pages

Published in:

Nucl.Phys.B 328 (1989) 753-776

Published: 1989

DOI:

10.1016/0550-3213(89)90229-0

Report number:

Print-89-0240 (BRITISH COLUMBIA)

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Abstract: (Elsevier)

Canonical quantization is used to examine the relationship between the addition of a Chern-Simons topological mass term to the action of a (2+1)-dimensional quantum field theory and exotic spin and statistics of elementary quanta. We argue that topologically massive electrodynamics is solved in the long wavelength limit by multi-valued fields with anomalous spin and which create quantum states which have exotic exchange statistics. The quantum states with N particles represent the braid group B N . We examine the implications of our results for the O(3) nonlinear sigma model where the topological current is coupled to topologically massive electrodynamics and the charge carriers are topological solitons.

field theory: topological
dimension: 3
path integral
Hamiltonian formalism
spin: statistics
statistics: fractional
sigma model: nonlinear
symmetry: O(3)
dimension: 2
field equations: soliton

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