Anyon in External Electromagnetic Field: Hamiltonian and Lagrangian Formulations

Abstract

We propose a simple model for a free relativistic particle of fractional spin in 2+1 dimensions which satisfies all the necessary conditions. The canonical quantization of the system leads to the description of one- particle states of the Poincare group with arbitrary spin. Using the Hamil- tonian formulation with the set of constraints, we introduce the electro- magnetic interaction of a charged anyon and obtain the Lagrangian. The Casimir operator of the extended algebra, which is the first-class constraint, is obtained and gives the equation of motion of the anyon. In particular, from the latter it follows that the gyromagnetic ratio for a charged anyon is two due to the parallelness of spin and momentum of the particle in 2+1 dimensions. The canonical quantization is also considered in this case.

9 pages, Latex, HU-SEFT R 1993-11

References in corpus (2)

• Equations of Motion for Spinning Particles in External\\Electromagnetic and Gravitational Fields
• On the Electromagnetic Interactions of Anyons

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• Constrained Dynamics of an Anomalous $(g/neq2)$ Relativistic Spinning Particle in Electromagnetic Background
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• Galilei Group with multiple central extension, vorticity and entropy generation: "Exotic" fluid in 3+1-dimensions
• Uncertainty Relations for the Relativistic Jackiw-Nair Anyon: A First Principles Derivation