A new approach to perturbation theory in the quantum phase-space formalism is proposed, in order to devise some approximated description of the quantum phase-space dynamics, which is not directly related to the usual semi-classical approximation. A general class of equivalent quasi-distribution functions based on the Wigner-Moyal formalism is considered and a first-order invariant formulation of the dynamics is obtained. The relationship between the various phase-space representations is expressed in term of a pseudo-differential operator defined by the Moyal product. In particular, our theory is applied to the sub-class of representations obtained by a first order perturbation of the Wigner representation. Finally the connection of our approach with some well established gauge-invariant formulations of the Wigner dynamics in the presence of an external magnetic field is investigated.
@article{BUMI_2011_9_4_1_1_0,
author = {Omar Morandi and Luigi Barletti and Giovanni Frosali},
title = {Perturbation Theory in Terms of a Generalized Phase-Space Quantization Procedure},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {4},
year = {2011},
pages = {1-18},
zbl = {1234.81078},
mrnumber = {2797463},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2011_9_4_1_1_0}
}
Morandi, Omar; Barletti, Luigi; Frosali, Giovanni. Perturbation Theory in Terms of a Generalized Phase-Space Quantization Procedure. Bollettino dell'Unione Matematica Italiana, Tome 4 (2011) pp. 1-18. http://gdmltest.u-ga.fr/item/BUMI_2011_9_4_1_1_0/
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