Non-abelian bosonization in two-dimensional condensed matter physics

We derive mathematical identities proving that some systems of interacting, non-relativistic fermions of spin or “isospin” S = 1 2 , 3 3 , 5 2 ,… confined to a plane (e.g. a heterojuncture) can be described in terms of a complex boson of spin or isospin S coupled to statistical U(1) and SU(2) gauge fields. In a Feynman path integral formulation, the U(1) gauge field has a Chern-Simons action with coupling constant k = 2 (2l + 1) , l = 0, 1, 2,… , while the SU(2) gauge field has a Chern-Simons action with level 2 S . Generalizations to internal symmetry groups other than SU(2) are sketched, and applications of our formalism to an analysis of excitations with braid statistics in incompressible quantum fluids and of holons and spinons in the t − J model are discussed.