Related papers: One-dimensional anyons in relativistic field theor…
We present new exact solutions (in 3+1 and 2+1 dimensions) of relativistic wave equations (Klein-Gordon and Dirac) in external electromagnetic fields of special form. These fields are combinations of Aharonov-Bohm solenoid field and some…
We construct a field theory for anyons in the lowest Landau level starting from the $N$-particle description, and discuss the connection to the full field theory of anyons defined using a statistical gauge potential. The theory is…
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 discuss the relation of the two types of sums in the Rogers-Schur-Ramanujan identities with the Bose-Fermi correspondence of massless quantum field theory in $1+1$ dimensions. One type, which generalizes to sums which appear in the…
Amplitudes for boson-boson and fermion-boson interactions are calculated in the second order of perturbation theory in the Lobachevsky space. An essential ingredient of the used model is the Weinberg's $2(2j+1)$ component formalism for…
We study a relativistic anyon model with a spin-$j$ matter field minimally coupled to a statistical gauge potential governed by the Chern-Simons dynamics with a statistical parameter $\alpha$. A spin and statistics transmutation is shown in…
Two-dimensional quantum field theories are important in many problems in physics because they contain exact symmetries and are often completely integrable. We demonstrate the power of bosonization in elucidating the structure of a…
We propose a new model for interacting (electrically charged) anyons, where the 2+1-dimensional Darwin term is responsible for interactions. The Hamiltonian is comparable with the one used previously (in the RPA calculation).
We show that abelian bosonization of 1+1 dimensional fermion systems can be interpreted as duality transformation and, as a conseguence, it can be generalized to arbitrary dimensions in terms of gauge forms of rank $d-1$, where $d$ is the…
The purpose of this overview article, which can be viewed as a supplement to our previous review on quantum rings, [S. Viefers {\it et al}, Physica E {\bf 21} (2004), 1-35], is to highlight the differences of boson and fermion systems in…
We discuss unifying features of topological field theories in 2, 3 and 4 dimensions. This includes relations among enumerative geometry (2d topological field theory) link invariants (3d Chern-Simons theory) and Donaldson invariants (4d…
We introduce bosonic (p - 1)-form fields that couple to the spin connection of the Einstein-Cartan theory of gravity thus becoming a non-trivial source of space-time torsion. We analyze all the general features of both the matter and the…
The problem of fermions in 1+1 dimensions in the presence of a pseudoscalar Coulomb potential plus a mixing of vector and scalar Coulomb potentials which have equal or opposite signs is investigated. We explore all the possible signs of the…
An arbitrary dimensional expression is given for the anomalous dimension of the fermion field in a model with a four point interaction and a $U(1)$ gauge field, at $O(1/N^2)$ within a large flavour expansion in the Landau gauge.
We show in three dimensions, using functional integral techniques, the equivalence between the partition functions of the massive Thirring model and a gauge theory with two gauge fields, to all orders in the inverse fermion mass. Detailed…
We gauge the abelian hierarchy of tensor fields in 4D by a Lie algebra. The resulting non-abelian tensor hierarchy can be interpreted via an equivariant chain complex. We lift this structure to N=1 superspace by constructing superfield…
The effective action of nonrelativistic fermions in 2+1 dimensions is analyzed at finite temperature and chemical potential in the presence of a uniform magnetic field perpendicular to the plane. The method used is a generalization of the…
We calculate some one loop corrections to the effective action of theories in $d$ dimensions that arise on the dimensional reduction of a Weyl fermion in $D$ dimensions. The terms that we are interested in are of a topological nature.…
We consider the many-particle quantum mechanics of anyons, i.e. identical particles in two space dimensions with a continuous statistics parameter $\alpha \in [0,1]$ ranging from bosons ($\alpha=0$) to fermions ($\alpha=1$). We prove a…
It is a long-standing question to extend the definition of 3-dimensional Chern-Simons theory to one which associates values to 1-manifolds with boundary and to 0-manifolds. We provide a solution in case the gauge group is a torus. We also…