CRITICAL PHENOMENON AND TOPOLOGICAL FIELD THEORIES IN THREE DIMENSIONS

Abstract

We give a new mechanism for Bose-Fermi transmutation based on phase transition in a renormalizable generalization of the three-dimensional CP 1 model coupled to a U(1) Chern-Simons theory. The generalization involves the addition of the scale invariant curvature term of the world line of the point particle. The short range disordered phase has a mass spectrum which corresponds to that of a single spinless bosonic point particle while the long range ordered phase has an infinite spinning Majorana mass spectrum. On the world line these Majorana particles have fermionic degrees of freedom.