TOPOLOGICAL QUANTUM MECHANICS IN 2+1 DIMENSIONS

Abstract

We show that the classical and quantum covariant dynamics of spinning particles in flat space in 2+1 dimensions are derived from a pure Wess-Zumino term written on the space of adjoint orbits of the ISO(2, 1) group. Similarly, the dynamics of spinning particles in 2+1 de Sitter [anti-de Sitter] space are derived from a Wess-Zumino term on the space of adjoint orbits of SO(3, 1) [SO(2, 2)]. It is shown that a quantum mechanical description of spin is possible in 2+1 dimensions without introducing explicit spin degrees of freedom, but at the expense of having a noncommutative space-time geometry.