On the Relativistic Field Theories with Fractional Statistics and Spin in D = (2 + 1), (3 + 1)

Abstract

Field theories in space-time dimensions D=(1,1), (2,1) (one time dimension and one or two space dimensions) possess some interesting features connected with the configuration space nontrivial topology of the systems concerned. For instance, solitons of D=2+1 theories can possess fractional charge, statistics and spin [1,2]. The experimental consequences of such peculiar properties can be obtained in condensed matter, where there are possibilities to realize two-dimensional systems. There is well known example of a fractionally quantized Hall effect [3.1]. The recent interest in (2+1)-dimensional theories and, particularly, in nonlinear σ-models has been triggered by the hope to describe the high temperature superconductivity phenomena [4].