The Magnetic Weyl Calculus

Details The Magnetic Weyl Calculus The Magnetic Weyl Calculus

2004-01-27

arxiv.org/abs/math-ph/0401043v1

Physics

Mathematical Physics

revised version of the preprint 03-498 on mp-arc accepted at Journal of Mathematical Physics

Scientific paper

10.1063/1.1668334

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.

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