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Gauge covariant formulation of Wigner representation through deformational quantization --Application to Keldysh formalism with electromagnetic field--

N. Sugimoto·S. Onoda·N. Nagaosa
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Abstract

We developed a gauge-covariant formulation of the non-equilibrium Green function method for the dynamical and/or non-uniform electromagnetic field by means of the deformational quantization method. Such a formulation is realized by replacing the Moyal product in the so-called Wigner space by the star product, and facilitates the order-by-order calculation of a gauge-invariant observable in terms of the electromagnetic field. An application of this formalism to the linear response theory is discussed.

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N. Sugimoto, S. Onoda, N. Nagaosa. 2006-11-06. Gauge covariant formulation of Wigner representation through deformational quantization --Application to Keldysh formalism with electromagnetic field--. https://doi.org/10.1143/ptp.117.415

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