Relativistic wave equation for anyons

Construction of one-particle states as unitary representations of the Poincare algebra in 2+1 dimensions shows that an anyon has one polarization state. However, for nonzero spin manifestly linear and covariant realizations of Lorentz transformations require more than one field component, and an inf...

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Bibliographic Details
Published in:Physical review. D, Particles and fields Particles and fields, 1991-03, Vol.43 (6), p.1933-1942
Main Authors: JACKIW, R, NAIR, V. P
Format: Article
Language:English
Subjects:
645201 - High Energy Physics- Particle Interactions & Properties-Theoretical- General & Scattering Theory
645400 - High Energy Physics- Field Theory
657003 - Theoretical & Mathematical Physics- Relativity & Gravitation
ANGULAR MOMENTUM
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Classical and quantum physics: mechanics and fields
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
Exact sciences and technology
FIELD EQUATIONS
FIELD THEORIES
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
INVARIANCE PRINCIPLES
LIE GROUPS
LORENTZ TRANSFORMATIONS
MATHEMATICAL MODELS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
PARTICLE PROPERTIES
PARTICLE STRUCTURE
Physics
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
POINCARE GROUPS
POLARIZATION
RELATIVITY THEORY
SIGMA MODEL
SPACE-TIME
SPIN
SYMMETRY
SYMMETRY GROUPS
THREE-DIMENSIONAL CALCULATIONS
TRANSFORMATIONS
WAVE EQUATIONS
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Summary:Construction of one-particle states as unitary representations of the Poincare algebra in 2+1 dimensions shows that an anyon has one polarization state. However, for nonzero spin manifestly linear and covariant realizations of Lorentz transformations require more than one field component, and an infinite number is needed when the value of spin is not an integer or half-integer. We discuss the relation between these two aspects of Poincare symmetry. In particular, we construct a relativistic equation for anyons where the number of physical polarizations is reduced to one by virtue of a gauge symmetry or equivalent constraint.
ISSN:0556-2821
1089-4918
DOI:10.1103/PhysRevD.43.1933