Low dimensional systems and anyonic statistics

Abstract

Anyonic statistics is a new knowledge in physics. It is based on the property of a configuration space to be multiply connected. This always happens in low dimensional systems, that is systems in two space dimensions. Also the anyonic statistics is based on the indistinguishability of particles. As a result of a symmetry exchange, that is, to exchange the position of two particles. In two dimensions the wavefunction acquires an non-trivial phase which is not the same as in the bosonic or fermionic statistics. This phase can be interpreted as an introduction of a gauge transformation in the lagrangian describing this system. Therefore, the anyons are particles that possess an extra type of “interaction”. Anyons are conceptualized as a charged particle with a flux associated. Thus quantum mechanics change for anyonic particles. The only possible phenomenological application of the anyonic statistics is the description of the FQHE where anyons are conceived as quasi-holes or quasi-particles, with fractional charge. Anyons then have reality in the sense that anyon particles are observable by the FQHE experiments.