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arXiv:1406.4578 · Journal of Statistical Mechanics Theory and Experiment

Duality and bosonization in Schwinger–Keldysh formulation

R E Gamboa Saraví, Carlos Naón, F Schaposnik

Published Sep 30, 2014• 2 citations
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Abstract

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.

DOI
10.1088/1742-5468/2014/09/p09034

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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.
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 extend a path-integral approach to bosonization previously developed in the framework of equilibrium Quantum Field Theories, to the case in which time-dependent interactions are taken into account. In particular we consider a non covariant version of the Thirring model in the presence of a dynamic barrier at zero temperature. By using the Closed Time Path (Schwinger-Keldysh) formalism, we compute the Green's function and the Total Energy Density of the system. Since our model contains the Tomonaga Luttinger model as a particular case, we make contact with recent results on non-equilibrium electronic systems.
We extend a path-integral approach to bosonization previously developed in the framework of equilibrium Quantum Field Theories, to the case in which time-dependent interactions are taken into account. In particular we consider a noncovariant version of the Thirring model in the presence of a dynamic barrier at zero temperature. By using the Closed Time Path (Schwinger–Keldysh) formalism, we compute the Green's function and the Total Energy Density of the system. Since our model contains the Tomonaga–Luttinger model as a particular case, we make contact with recent results on nonequilibrium electronic systems.