Luigi Pilo — Page 3

arXiv1999

Anyon Condensation and Persistent Currents

In this letter we study 1+1 anyon fields at finite temperature and density with non-vanishing chemical potentials. Our approach is based on an operator formalism for bosonization at finite temperature; the correlation functions for the system are given in an explicit form. Two are the main results of this construction: we point out the existence of persistent currents in 1+1 anyon systems; from the analysis of 2-point anyon field correlation function, a remarkable and new condensation phenomenon in momentum space is discovered. As a concrete example, the above formalism is applied to the Thirring model.

hep-th↗

arXiv1998

Chern-Simons field theory and invariants of 3-manifolds

The Chern-Simons (CS) theory in three dimensions with a compact gauge group G is studied. Starting from the BRST quantization of the theory defined in R^3, the values of gauge invariants observables are computed in any closed and orientable three manifold M by constructing a surgery operator associated with a Dehn's surgery presentation of M. We have given the general rules to find the reduced tensor algebra whose elements give the physical inequivalent quantum numbers that characterize uniquely the CS observables. Some general properties of the reduced tensor algebra and of the surgery operator are studied. Many examples of the general construction are given in the case of G=SU(2) and G=SU(3), in particular the expectation value of a Wilson line associated with the unknot and the Hopf link in R^3(S^3) is computed for any irreducible representation of the gauge group. The relation of the topological invariant I(M), defined as a suitable modified partition function of the CS theory in M, and the fundamental group of M is studied. Finally, the relationship between CS theory and WZWN model in two dimensions is exploited to derive from a full three-dimensional point of view some classical results in conformal field theory.

hep-th↗