Marius Mantoiu, Radu Purice
The Magnetic Weyl Calculus
(642K, ps)

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.