Gradient expansion of the non-Abelian gauge-covariant Moyal star-product
| Autor: | Konschelle, François |
|---|---|
| Přispěvatelé: | Centre Hospitalier Universitaire de Bordeaux (CHU de Bordeaux) |
| Rok vydání: | 2021 |
| Předmět: |
Quantum Physics
Statistical Mechanics (cond-mat.stat-mech) phase-space quantum mechanics Condensed Matter - Superconductivity High Energy Physics::Lattice Keywords: Moyal star product FOS: Physical sciences non-Abelian gauge theory [PHYS.COND.CM-S]Physics [physics]/Condensed Matter [cond-mat]/Superconductivity [cond-mat.supr-con] Superconductivity (cond-mat.supr-con) effective theory semi-classic and quasi-classic approximation Wigner transform High Energy Physics::Theory gradient expansion topological field theory [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] strict quantisation kinetic theory deformation quantisation [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] Quantum Physics (quant-ph) Condensed Matter - Statistical Mechanics quantum transport |
| DOI: | 10.48550/arxiv.2111.01497 |
| Popis: | Motivated by the recent developments of gauge-covariant methods in the phase-space, a systematic method is presented aiming at the generalisation of the Moyal star-product to a non-Abelian gauge covariant one at any order. Such an expansion contains some dressing of the bare particle model by the gauge-fields explicitly, and might serve as a drastically simplifying tool for the elaborations of gauge-covariant quantum transport models. In addition, it might be of fundamental importance for the mathematical elaborations of gauge theory using the strict or deformation quantisation principles. A few already known examples of quantum kinetic theories are recovered without effort as an illustration of the power of this tool. A gauge-covariant formulation taking into account possible geometrical connections in both the position and momentum spaces is also constructed at leading orders, with applications to the generation of gauge-covariant effective theories in the phase-space. This paper is devoted to the pedestrian elaboration of the gradient expansions. Their numerous consequences will be explored in subsequent works. |
| Databáze: | OpenAIRE |
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