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.
Highlights
Bosonization is a powerful technique, widely used to analyze quantum systems in one spatial dimension [1]
The path-integral approach originally developed for bosonization in D = 2 space-time dimensions as a particular case of a duality transformation [11]-[12] has been very successful because it allows to simple extensions to D > 2 dimensions
The duality process amounts to gauging the global symmetry of the original theory, and constraining the corresponding field strength to vanish by introducing a Lagrange multiplier that is identified as the dual bosonic field. In this way one can find for example that in the large mass limit of a D = 3 fermionic theory bosonization leads to a Chern-Simons model, this leading to the existence of operators of the Fermi theory which ought to exhibit fractional statistics [12]
Summary
Bosonization is a powerful technique, widely used to analyze quantum systems in one spatial dimension [1]. Our proposal is inspired in the ”target space duality” of string theory [13], and can be applied in any number of space dimensions, leading to exact results for Abelian and non-Abelian bosonization of massive and massless Dirac fermions in 1 + 1 space-time dimension and perturbative answers in d > 1 space dimensions We find that this path-integral bosonization framework is appropriate when considering out of equilibrium systems using the Schwinger-Keldysh time closed contour technique [14]-[18] leading to very natural extensions of the Coleman-Mandelstam bosonization recipe [2]. GENERATING FUNCTIONAL FOR FREE DIRAC FERMIONS IN THE SCHWINGER-KELDYSH TIME CLOSED PATH
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