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The magnetic Weyl calculus. (English) Zbl 1068.81043

Summary: 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 formulas 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.

MSC:

81S99 General quantum mechanics and problems of quantization
53D55 Deformation quantization, star products
81Q99 General mathematical topics and methods in quantum theory
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