Covariant Weyl quantization, symbolic calculus, and the product formula

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Title: Covariant Weyl quantization, symbolic calculus, and the product formula
Author: Gunturk, Kamil Serkan
Abstract: A covariant Wigner -Weyl quantization formalism on the manifold that uses pseudo -differential operators is proposed . The asymptotic product formula that leads to the symbol calculus in the presence of gauge and gravitational fields is presented . The new definition is used to get covariant differential operators from momentum polynomial symbols . A covariant Wigner function is defined and shown to give gauge -invariant results for the Landau problem . An example of the covariant Wigner function on the 2 -sphere is also included .
URI: http : / /hdl .handle .net /1969 .1 /3963
Date: 2006-08-16

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Covariant Weyl quantization, symbolic calculus, and the product formula. Available electronically from http : / /hdl .handle .net /1969 .1 /3963 .

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