We derive mathematical identities proving that some systems of interacting, non-relativistic fermions of spin or “isospin” View the MathML source 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 View the MathML source, while the SU(2) gauge field has a Chern-Simons action with level 2S. 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.
Non abelian bosonization in two-dimensional condensed matter physics.
MARCHETTI, PIERALBERTO
1992
Abstract
We derive mathematical identities proving that some systems of interacting, non-relativistic fermions of spin or “isospin” View the MathML source 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 View the MathML source, while the SU(2) gauge field has a Chern-Simons action with level 2S. 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.
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