Gauge Covariant Formulation of the Wigner Representation through Deformation Quantization: Application to Keldysh Formalism with an Electromagnetic Field | Zendy

Naoyuki Sugimoto | Zendy; Satoshi Onoda | Zendy; Naoto Nagaosa | Zendy

Open Access

Gauge Covariant Formulation of the Wigner Representation through Deformation Quantization: Application to Keldysh Formalism with an Electromagnetic Field

Author(s) -

Naoyuki Sugimoto,

Satoshi Onoda,

Naoto Nagaosa

Publication year - 2007

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.117.415

Subject(s) - physics , covariant transformation , electromagnetic field , quantization (signal processing) , gauge theory , star product , wigner distribution function , observable , mathematical physics , mathematical descriptions of the electromagnetic field , classical mechanics , formalism (music) , gauge fixing , quantum electrodynamics , quantum mechanics , gauge boson , quantum , art , musical , visual arts , mathematics , combinatorics , computer science , computer vision

We developed a gauge-covariant formulation of the non-equilibrium Greenfunction method for the dynamical and/or non-uniform electromagnetic field bymeans of the deformational quantization method. Such a formulation is realizedby replacing the Moyal product in the so-called Wigner space by the starproduct, and facilitates the order-by-order calculation of a gauge-invariantobservable in terms of the electromagnetic field. An application of thisformalism to the linear response theory is discussed

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