Interacting anyons and the Darwin Lagrangian

In their recent letter, Chaichian et.~al. present a Lagrangian for a massive ($m$) point particle on the plane, with which they claim to realize anyon statistics. However, we find that there are some inaccuracies in their formulation and, when these are taken care of, well-known results are reproduced, which already exist in the literature.

We point out that in a recent paper by Chaichian et al. (Phys. Rev.Lett71(1993)3405) Dirac quantization procedure is not properly followed as a result of which the resulting quantum theory is different from what one will get by a straightforward application of Dirac's formulation. For example at quantum level the model in I has noncommutative geometry, i.e., $[x_\mu, x_\nu] \neq 0$ while a correct treatment would give $[x_\mu, x_\nu] = 0$. Moreover, their assertion about $\al...

We discuss how to construct models of interacting anyons by generalizing quantum spin Hamiltonians to anyonic degrees of freedom. The simplest interactions energetically favor pairs of anyons to fuse into the trivial ("identity") channel, similar to the quantum Heisenberg model favoring pairs of spins to form spin singlets. We present an introduction to the theory of anyons and discuss in detail how basis sets and matrix representations of the interaction terms can be obtaine...

In this paper we explore some surprising consequences of the retardation effects of Maxwell's electrodynamics to a system of charged particles. The specific cases of three interacting particles are considered in the framework of classical electrodynamics. We show that the solutions of the equations of motion defined by the Darvin Lagrangian in some cases contradict to common sense.

One-dimensional anyon models are renewedly constructed by using path integral formalism. A statistical interaction term is introduced to realize the anyonic exchange statistics. The quantum mechanics formulation of statistical transmutation is presented.

In two spatial dimensions, spin characterizes how particle states re-phase under changes of frame that leave their momentum and energy invariant. Massless particles can in principle have non-trivial spin in this sense, but all existing field theories only describe the trivial case. This letter presents a field theory for a massless particle with non-trivial physical spin. These particles are the 2+1-dimensional analogues of "continuous-spin" particles in 3+1 dimensions, but h...

In this article we develop a general method to numerically calculate physical properties for a system of anyons with path integral molecular dynamics. We provide a unified method to calculate the thermodynamics of identical bosons, fermions and anyons. Our method is tested and applied to systems of anyons, bosons and fermions in a two-dimensional harmonic trap. We also consider a method to calculate the energy for fermions as an application of the path integral molecular dyna...

We propose a transformation for spin and charge degrees of freedom in one-dimensional lattice systems, constrained to have no doubly occupied sites, that allows direct access to the dynamical correlations of the system. The transformation delivers particle creation and annihilation operators in a form of a spinless particle and a non-local operator acting on the space of states of a spin-$1/2$ chain. This permits a decomposition of dynamical correlation functions as a convolu...

(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.

It is shown that the scattering amplitude for contact-interacting anyons does exhibit a genuine non-perturbative sector. This means that the corresponding perturbative field theoretical formulation, based on the {\it 2+1} non-relativistic Chern-Simons gauge model coupled to self-interacting complex scalar field, is not generally able to reproduce, order by order in perturbation theory, the exact result. It is proven that the full agreement between the exact scattering amplitu...