Zampini, Alessandro (2005) Application of the Weyl-Wigner formalism of noncommutative geometry. [Tesi di dottorato] (Unpublished)
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|Item Type:||Tesi di dottorato|
|Uncontrolled Keywords:||Noncommutative geometry, Weyl-Wigner formalism, Fuzzy disc|
|Date Deposited:||01 Aug 2008|
|Last Modified:||30 Apr 2014 19:22|
In this dissertation the Weyl-Wigner approach is presented as a map between funcions on a real cartesian sympletic 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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