03-498 Marius Mantoiu, Radu Purice

The Magnetic Weyl Calculus (642K, ps) Nov 13, 03

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Abstract. In the presence of a variable magnetic field, the Weyl pseudodifferential calculus must be modidfied. 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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