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AIP conference proceedings

Fermionic current algebra in three dimensions

Carlos Núñez

Published Jan 1, 1998• 0 citations
Publisher

Abstract

We consider the fermion-boson mapping in three dimensional space-time, in the Abelian case, from the current algebra point of view. It is shown that in a path-integral framework one can derive a general bosonization recipe leading, in the bosonic language, to the correct equal-time current commutators of the original free fermionic theory.

DOI
10.1063/1.54703

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We consider the fermion-boson mapping in three dimensional space-time, in the Abelian case, from the current algebra point of view. It is shown that in a path-integral framework one can derive a general bosonization recipe leading, in the bosonic language, to the correct equal-time current commutators of the original free fermionic theory.
We present a path-integral bosonization approach for systems out of equilibrium based on a duality transformation of the original Dirac fermion theory combined with the Schwinger-Keldysh time closed contour technique, to handle the non-equilibrium situation. The duality approach to bosonization that we present is valid for D 2 space-time dimensions leading for D = 2 to exact results. In this last case we present the bosonization rules for fermion currents, calculate current-current correlation functions and establish the connection between the fermionic and bosonic distribution functions in a generic, nonequilibrium situation.
We present a new bosonization procedure for two-dimensional fermion models in the path integral formulation. We introduce external sources for the fermion currents instead of the auxiliary boson fields used in the conventional procedure. The calculations become much simpler because the external sources do not interact with themselves, while the auxiliary boson fields do, and we can find the equivalent boson models directy. All the formulations are done in Minkowski space-time. The extended Bukhvostov-Lipatov model and the massive Thirring model are discussed here as typical two-dimensional fermion models with current-current-type interactions. The Rothe and Stamatescu model is also discussed, though this is slightly out of the context of bosonization, and the relation of the fermion current in the Heisenberg picture with that in the interaction picture is derived almost straightforwardly. Usually in the operator formalism, this relation is derived using the splitting procedure, which requires detailed calculations. It is expected that we can derive the boson model equivalent to the fermion model with SU(N) symmetry more easily and without any guess work.
We present a path-integral bosonization approach for systems out of equilibrium based on a duality transformation of the original Dirac fermion theory combined with the Schwinger–Keldysh time closed contour technique, to handle the non-equilibrium situation. The duality approach to bosonization that we present is valid for D ≥ 2 space–time dimensions leading for D = 2 to exact results. In this last case we present the bosonization rules for fermion currents, calculate current–current correlation functions and establish the connection between the fermionic and bosonic distribution functions in a generic, non-equilibrium situation.