Anyons, group theory and planar physics (original) (raw)
Related papers
On the Geometry of Relativistic Anyon
Modern Physics Letters A, 1997
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 leads to the anyon model with free phase space which 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 Poincaré group.
Non-relativistic anyons and exotic Galilean symmetry
arXiv (Cornell University), 2002
We show that the Lukierski et al. model, invariant with respect to the twofold centrally extended Galilei group, can be decomposed into an infinite number of independent copies (differing in their spin) of the "exotic" particle of Duval et al. The difference between the two models is found to be sensitive to electromagnetic coupling. The nature of the noncommutative plane coordinates is discussed in the light of the exotic Galilean symmetry. We prove that the first model, interpreted as describing a non-relativistic anyon, is the non-relativistic limit of a particle with torsion related to relativistic anyons.
Non-relativistic anyons, exotic Galilean symmetry and noncommutative plane
Journal of High Energy Physics, 2002
We show that the Lukierski et al. model, invariant with respect to the two-fold centrally extended Galilei group, can be decomposed into an infinite number of independent copies (differing in their spin) of the "exotic" particle of Duval et al. The difference between the two models is found to be sensitive to electromagnetic coupling. The nature of the noncommutative plane coordinates is discussed in the light of the exotic Galilean symmetry. We prove that the first model, interpreted as describing a non-relativistic anyon, is the non-relativistic limit of a particle with torsion related to relativistic anyons.
Anyons as spin particles: from classical mechanics to field theory
1995
(2+1)-dimensional relativistic fractional spin particles are considered within the framework of the group-theoretical approach to anyons starting from the level of classical mechanics and concluding by the construction of the minimal set of linear differential field equations.
Journal of Mathematical Physics, 1990
This paper is devoted to the study of the description of elementary physical systems interacting with an external constant electromagnetic field and the construction of their differential wave equations from a group-theoretical point of view. In this context certain local realizations of the Poincare group are studied. The linearization of this problem is carried out by building the associated representation group that turns out to be the well-known Maxwell group. In this way the usual method (concerning local realizations) that has been employed in studying free systems to the interacting case is extended.
Comments on spin-orbit interaction of anyons
Mod Phys Lett a, 2005
The coupling of nonrelativistic anyons (called exotic particles) to an electromagnetic field is considered. Anomalous coupling is introduced by adding a spin-orbit term to the Lagrangian. Alternatively, one has two Hamiltonian structures, obtained by either adding the anomalous term to the Hamiltonian, or by redefining the mass and the NC parameter. The model can also be derived from its relativistic counterpart.
Enlarged Galilean symmetry of anyons and the Hall effect
Physics Letters B, 2005
Enlarged planar Galilean symmetry, built of both space-time and field variables and also incorporating the "exotic" central extension is introduced. It is used to describe nonrelativistic anyons coupled to an electromagnetic field. Our theory exhibits an anomalous velocity relation of the type used to explain the Anomalous Hall Effect. The Hall motions, characterized by a Casimir of the enlarged algebra, become mandatory for some critical value(s) of the magnetic field. The extension of our scheme yields the semiclassical effective model of the Bloch
Electromagnetic Interaction of Anyons in NonRelativistic Quantum Field Theory
1992
The non-relativistic quantum field theoretic lagrangian which describes an anyon system in the presence of an electromagnetic field is identified. A non-minimal magnetic coupling to the Chern-Simons statistical field as well as to the electromagnetic field together with a direct coupling between between both fields are the non-trivial ingredients of the lagrangian obtained from the non-relativistic limit of the fermionic relativistic formulation. The results, an electromagnetic gyromagnetic ratio 2 for any spin together with a non-trivial dynamical spin dependent contact interaction between anyons as well as the spin dependence of the electromagnetic effective action, agree with the quantum mechanical formulation.
Electromagnetic interaction of anyons
Physics Letters B, 1992
A U(1) gauge theory of a particle with arbitrary spin in three spacetime dimensions is introduced. All the spin dependent effects are a consequence ofa Chern-Simons field which is coupled to a conserved current with a piece involving the U (1) gauge field. In the case of a spin-½ particle one reproduces all the results of the spinning particle in the presence of an electromagnetic field.
Diffeomorphism groups and anyon fields
1995
We make use of unitary representations of the group of diffeomorphisms of the plane to construct an explicit field theory of anyons. The resulting anyon fields satisfy q-commutators, where q is the well-known phase shift associated with a single counterclockwise exchange of a pair of anyons. Our method uses a realization of the braid group by means of paths in the plane, that transform naturally under diffeomorphisms of R².