6 research outputs found
Fractional Exclusion Statistics and Anyons
Do anyons, dynamically realized by the field theoretic Chern-Simons
construction, obey fractional exclusion statistics? We find that they do if the
statistical interaction between anyons and anti-anyons is taken into account.
For this anyon model, we show perturbatively that the exchange statistical
parameter of anyons is equal to the exclusion statistical parameter. We obtain
the same result by applying the relation between the exclusion statistical
parameter and the second virial coefficient in the non-relativistic limit.Comment: 9 pages, latex, IFT-498-UN
Algebraic Quantization, Good Operators and Fractional Quantum Numbers
The problems arising when quantizing systems with periodic boundary
conditions are analysed, in an algebraic (group-) quantization scheme, and the
``failure" of the Ehrenfest theorem is clarified in terms of the already
defined notion of {\it good} (and {\it bad}) operators. The analysis of
``constrained" Heisenberg-Weyl groups according to this quantization scheme
reveals the possibility for new quantum (fractional) numbers extending those
allowed for Chern classes in traditional Geometric Quantization. This study is
illustrated with the examples of the free particle on the circumference and the
charged particle in a homogeneous magnetic field on the torus, both examples
featuring ``anomalous" operators, non-equivalent quantization and the latter,
fractional quantum numbers. These provide the rationale behind flux
quantization in superconducting rings and Fractional Quantum Hall Effect,
respectively.Comment: 29 pages, latex, 1 figure included with EPSF. Revised version with
minor changes intended to clarify notation. Acepted for publication in Comm.
Math. Phy
Fock Representations of Quantum Fields with Generalized Statistic
We develop a rigorous framework for constructing Fock representations of
quantum fields obeying generalized statistics associated with certain solutions
of the spectral quantum Yang-Baxter equation. The main features of these
representations are investigated. Various aspects of the underlying
mathematical structure are illustrated by means of explicit examples.Comment: 26 pages, Te
Vortices on Higher Genus Surfaces
We consider the topological interactions of vortices on general surfaces. If
the genus of the surface is greater than zero, the handles can carry magnetic
flux. The classical state of the vortices and the handles can be described by a
mapping from the fundamental group to the unbroken gauge group. The allowed
configurations must satisfy a relation induced by the fundamental group. Upon
quantization, the handles can carry ``Cheshire charge.'' The motion of the
vortices can be described by the braid group of the surface. How the motion of
the vortices affects the state is analyzed in detail.Comment: 28 pages with 10 figures; uses phyzzx and psfig; Caltech preprint
CALT-68-187
Thermodynamics of an Anyon System
We examine the thermal behavior of a relativistic anyon system, dynamically
realized by coupling a charged massive spin-1 field to a Chern-Simons gauge
field. We calculate the free energy (to the next leading order), from which all
thermodynamic quantities can be determined. As examples, the dependence of
particle density on the anyon statistics and the anyon anti-anyon interference
in the ideal gas are exhibited. We also calculate two and three-point
correlation functions, and uncover certain physical features of the system in
thermal equilibrium.Comment: 18 pages; in latex; to be published in Phys. Rev.