The Magnetic Weyl Calculus
Mathematical Physics
2013-04-10 v1 Functional Analysis
math.MP
Abstract
In the presence of a variable magnetic field, the Weyl pseudodifferential calculus must be modified. The usual modification, based on ``the minimal coupling principle'' at the level of the classical symbols, does not lead to gauge invariant formulae if the magnetic field is not constant. We present a gauge covariant quantization, relying on the magnetic canonical commutation relations. The underlying symbolic calculus is a deformation, defined in terms of the magnetic flux through triangles, of the classical Moyal product.
Cite
@article{arxiv.math-ph/0401043,
title = {The Magnetic Weyl Calculus},
author = {Marius Mantoiu and Radu Purice},
journal= {arXiv preprint arXiv:math-ph/0401043},
year = {2013}
}
Comments
revised version of the preprint 03-498 on mp-arc accepted at Journal of Mathematical Physics