ar X iv : h ep - t h / 97 04 18 2 v 1 2 5 A pr 1 99 7 On the Geometry of Relativistic Anyon
نویسنده
چکیده
A twistor model is proposed for the free relativistic anyon. The Hamiltonian reduction of this model by the action of the spin generator leads to the minimal covariant model; whereas that by the action of spin and mass generators, to the anyon model with free phase space that is a cotangent bundle of the Lobachevsky plane with twisted symplectic structure. Quantum mechanics of that model is described by irreducible representations of the (2+1)-dimensional Poincare' group. 1. Introduction. As is known, in (2+1)-dimensional space-time there can exist anyons, particles with arbitrary spins and statistics [1]. Quantum mechanics of anyons as a spinning particles is described by unitary irreducible representations of the (2+1)-dimensional Poincare' group [2]. However, classical theory of anyons cannot be described within the standard approach based on the introducing of Grassmann variables. For this purpose are use the so-called " minimal " and " extended " approaches (here me employ the classification of Ref.[3]). In the minimal approach, the spin is provided by the nontrivial symplectic structure of phase space [4, 2]. The minimal relativistic-covariant model (in what follows, K−model) of the anyon with spin s is realized on the phase space T * IR 1.2 with the twisted symplectic structure g ab dP a ∧ dQ b + s P
منابع مشابه
ar X iv : h ep - t h / 97 04 18 2 v 3 3 0 A pr 1 99 7 On the Geometry of Relativistic Anyon
A twistor model is proposed for the free relativistic anyon. The Hamiltonian reduction of this model by the action of the spin generator leads to the minimal covariant model; whereas that by the action of spin and mass generators, to the anyon model with free phase space that is a cotangent bundle of the Lobachevsky plane with twisted symplectic structure. Quantum mechanics of that model is des...
متن کاملar X iv : h ep - t h / 97 04 15 5 v 1 2 2 A pr 1 99 7 KANAZAWA - 97 - 04 Abelian Projection of SU ( 2 ) Gluodynamics and Monopole Condensate ∗
The general properties of the abelian projection are reviewed. We derive the explicit expression for the abelian functional integral for U(1) abelian theory which corresponds to the abelian projection of the SU(2) gluodynamics. The numerical results for the temperature dependence of the monopole condensate are presented.
متن کاملar X iv : h ep - p h / 97 04 41 7 v 1 2 8 A pr 1 99 7 Associated Production of Hγ or HZ pairs at μ + μ − Collisions
متن کامل
ar X iv : h ep - t h / 93 04 10 3 v 1 2 2 A pr 1 99 3 EHU - FT - 93 April 1993 THREE - LOOP CALCULATION OF THE ANYONIC FULL CLUSTER EXPANSION
We calculate the perturbative correction to every cluster coefficient of a gas of anyons through second order in the anyon coupling constant, as described by Chern-Simons field theory.
متن کامل