Interacting anyons and the Darwin Lagrangian

In this paper we discuss the principles of measuring topological charge or representation traveling in the set of anyons. We describe the procedure and analyze how it works for the different values of parameters of the theory. We also show how it can be modified to be more effective for different levels of Chern-Simons theory.

We define a Chern- Simons Lagrangian for a system of planar particles topologically interacting at a distance. The anyon model appears as a particular case where all the particles are identical. We propose exact N-body eigenstates, set up a perturbative algorithm, discuss the case where some particles are fixed on a lattice, and also consider curved manifolds. PACS numbers: 05.30.-d, 11.10.-z

In the semiclassical approximation of Grassmann-valued electric charges for regularizing Coulomb self-energies, we extract the unique acceleration-independent interaction hidden in any Lienard-Wiechert solution for the system of N positive-energy spinning particles plus the electromagnetic field in the radiation gauge of the rest-frame instant form. With the help of a semiclassical Foldy-Wouthuysen transformation, this allows us to find the relativistic semiclassical Darwin p...

In these lectures several aspects of anyon in one and two dimensions are considered from the path integral formalism. This paper is based in a set of four lectures given by the author in the "V Latinoamerican Workshop of Particles and Fields, hel in Puebla, Mexico.

It is shown that a recently proposed relativistic field theory of anyons is mathematically flawed and also does not satisfy reasonable criteria for such a theory.

We extend the standard solid-state quantum mechanical Hamiltonian containing only Coulomb interactions between the charged particles by inclusion of $1/c^2$ terms representing (transverse) current-current interaction. For its derivation we use the classical formulation of Landau-Lifshitz, however consequently in the Coulomb gauge. Our Hamiltonian does not coincide with the Darwin Hamiltonian and we emphasize the mathematical inconsistency in its derivation. We show, that the ...

This article gives a pedagogic derivation of the Bethe Ansatz solution for 1D interacting anyons. This includes a demonstration of the subtle role of the anyonic phases in the Bethe Ansatz arising from the anyonic commutation relations. The thermodynamic Bethe Ansatz equations defining the temperature dependent properties of the model are also derived, from which some groundstate properties are obtained.

All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations are also obtained via contractions of the corresponding representations of the Lorentz group. Finally the obtained representations are used to derive a general Pauli anomalous interaction term and Darwin and spin-orbit couplings of a Galile...

One of the interesting fundamental phenomenon which was observed in the last decades is the discovery of anyons, relativistic spinning particles in $2+1$ dimensions. In contrast to three-dimensional space, indistinguishable quantum particles in two-dimensional space can, in general, have anomalous statistics [1-4]. These quasiparticles carry not only a charge $q$ also the magnetic flux $\Phi_0$.

In this set of lectures, we give a pedagogical introduction to the subject of anyons. We discuss 1) basic concepts in anyon physics, 2) quantum mechanics of two anyon systems, 3) statistical mechanics of many anyon systems, 4) mean field approach to many anyon systems and anyon superconductivity, 5) anyons in field theory and 6) anyons in the Fractional Quantum Hall Effect (FQHE). (Based on lectures delivered at the VII SERC school in High Energy Physics at the Physical Resea...