Applications of the Weyl-Wigner formalism to noncommutative geometry

Details Applications of the Weyl-Wigner formalism to noncommutative geometry Applications of the Weyl-Wigner formalism to noncommutative geometry

2005-05-31

arxiv.org/abs/hep-th/0505271v1

Physics

High Energy Physics

High Energy Physics - Theory

102 pages, 10 figures, Ph.D. Thesis

Scientific paper

In this dissertation the Weyl-Wigner approach is presented as a map between functions on a real cartesian symplectic vector space and a set of operators on a Hilbert space, to analyse some aspects of the relations between quantum and classical formalism, both as a quantization, and as a classical limit. It is presented an extension of this formalism to the case of a more general classical phase space, namely one whose configuration space is a compact simple Lie group. In the second part, it is used to develop a fuzzy approximation to the algebra of functions on a disc. This is the first example of a fuzzy space originating from a classical space which has a boundary. It is analysed how this approximation copes the presence of ultraviolet divergences even in noninteracting field theories on a disc.

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