A New Theory of Anyons

1999

The question of anyons and fractional statistics in field theories in 2+1 dimensions with Chern-Simons (CS) term is discussed in some detail. Arguments are spelled out as to why fractional statistics is only possible in two space dimensions. This phenomenon is most naturally discussed within the framework of field theories with CS term, hence as a prelude to this discussion I first discuss the various properties of the CS term. In particular its role as a gauge field mass term is emphasized. In the presence of the CS term, anyons can appear in two different ways i.e. either as soliton of the corresponding field theory or as a fundamental quanta carrying fractional statistics and both approaches are elaborated in some detail.

1996

We consider the analog in one spatial dimension of the Bose-Fermi transmutation for planar systems. That is, the construction of a purely bosonic effective local theory starting from a system of bosons and fermions upon integration over the fermionic variables. We consider a quantum mechanical system of a spin 1/2 particle coupled to an abelian gauge field, which is classically invariant under gauge transformations and charge conjugation. It is found that, unless the flux enclosed by the particle orbits is quantized, and the spin takes a value n + 1/2, at least one of the two symmetries would be anomalous. Thus, charge conjugation invariance and the existence of abelian instantons simultaneously avoid the anomaly and force the particles to be

Physics Letters B, 1990

We discuss the role of fractional statistics in determining the vacuum of a quantum field theory in 2+ 1 dimensions and show that the 0 parameter for anyons may be determined dynamically, by the presence of a non-zero fermion condensate at finite temperature. By choosing appropriate boundary conditions, in a simplified model, the result suggests that pointlike vortices would have 3n statistics to first order in perturbation theory on the grounds of least energy. The notion of anyons with non-abelian statistics is also considered, and it is shown that the statistics gauge group can be broken by the analogue of the Hosotani mechanism, so that there may be domains of statistics around vortices as well as Yang-Mills domains. We speculate on possible observable implications of our results.

Physics Letters B, 1995

The possibility of excitations with fractional spin and statististics in 1 + 1 dimensions is explored. The configuration space of a two-particle system is the half-line. This makes the Hamiltonian self-adjoint for a family of boundary conditions parametrized by one real number γ. The limit γ → 0, (∞) reproduces the propagator of non-relativistic particles whose wavefunctions are even (odd) under particle exchange. A relativistic ansatz is also proposed which reproduces the correct Polyakov spin factor for the spinning particle in 1 + 1 dimensions. These checks support validity of the interpretation of γ as a parameter related to the "spin" that interpolates continuously between bosons (γ = 0) and fermions (γ = ∞). Our approach can thus be useful for obtaining the propagator for one-dimensional anyons.

1991

We obtain a hierarchy of effective Hamiltonians which allow for a unified treatment of the fractional quantum Hall effect and a gas of fractional-statistics particles (anyons) in two dimensions. Anyon superconductivity is the analog of the fractional quantum Hall effect. For a rational statistics parameter a, P/Q with PQ even, Q anyons bind forming a charge-Qe superfluid.

1996

We consider the analog in one spatial dimension of the Bose-Fermi transmutation for planar systems. That is, the construction of a purely bosonic effective local theory starting from a system of bosons and fermions upon integration over the fermionic variables. We consider a quantum mechanical system of a spin 1/2 particle coupled to an abelian gauge field, which is classically invariant under gauge transformations and charge conjugation. It is found that, unless the flux enclosed by the particle orbits is quantized, and the spin takes a value n + 1/2, at least one of the two symmetries would be anomalous. Thus, charge conjugation invariance and the existence of abelian instantons simultaneously avoid the anomaly and force the particles to be

Physical Review A, 2004

We show that bosonic fields may present anyonic behavior when interacting with a fermion in a Jaynes-Cummings-like model. The proposal is accomplished via the interaction of a two-level system with two quantized modes of a harmonic oscillator; under suitable conditions, the system acquires a fractional geometric phase. A crucial role is played by the entanglement of the system eigenstates, which provides a twodimensional confinement in the effective evolution of the system, leading to the anyonic behavior. For a particular choice of parameters, we show that it is possible to transmute the statistics of the system continually from fermions to bosons. We also present an experimental proposal, in an ion-trap setup, in which fractional statistical features can be generated, controlled, and measured.

2021

We show that in spinor-helicity variables, two-point and three-point functions in Chern-Simons matter theories can be obtained from either the free boson theory or the free fermion theory with an appropriate coupling constant dependent anyonic phase factor which interpolates nicely between the free fermion theory and the free boson theory. For specific examples of four-point functions involving spinning operators we argue that the correlators can again be reproduced from the free theory with an appropriate phase factor. ar X iv :2 10 6. 09 04 3v 3 [ he pth ] 8 J ul 2 02 1

Physics Letters B, 1991

We consider systems containing two or more distinct species of particles in two spatial dimensions. In quantizations of these systems, the statistics of composites containing more than one type of particle are not completely determined by the statistics of the constituents. In particular there exist quantum theories in which two bosons can combine to form an anyon with any desired statistical angle. We demonstrate these results using the topological approach to quantum kinematics, which in this case leads to a generalization of ordinary braid theory in two dimensions. Comparisons are made to three-dimensional systems.

Communications in Mathematical Physics, 1989

We develop the quantization of topological solitons (vortices) in three-dimensional quantum field theory, in terms of the Euclidean region functional integral. We analyze in some detail the vortices of the abelian Higgs model. If a Chern-Simons term is added to the action, the vortices turn out to be "anyons," i.e. particles with arbitrary real spin and intermediate (Θ) statistics. Localization properties of the interpolating field, scattering theory and spin-statistics connection of anyons are discussed. Such analysis might be relevant in connection with the fractional quantum Hall effect and twodimensional models of High T c superconductors.