Extension of explicit formulas in Poissonian white noise analysis using harmonic analysis on configuration spaces

Harmonic analysis on configuration spaces is used in order to extend explicit expressions for the images of creation, annihilation, and second quantization operators in L2-spaces with respect to Poisson point processes to a set of functions larger than the space obtained by directly using chaos expa...

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Bibliographic Details
Published in:Condensed matter physics 2008-01, Vol.11 (2), p.237
Main Authors: Kondratiev, Kuna, Oliveira
Format: Article
Language:English
Subjects:
annihilation operators
chaos decomposition
configuration spaces
creation operators
Poisson measures
second quantization operators
Online Access:Get full text
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Summary:Harmonic analysis on configuration spaces is used in order to extend explicit expressions for the images of creation, annihilation, and second quantization operators in L2-spaces with respect to Poisson point processes to a set of functions larger than the space obtained by directly using chaos expansion. This permits, in particular, to derive an explicit expression for the generator of the second quantization of a sub-Markovian contraction semigroup on a set of functions which forms a core of the generator.
ISSN:1607-324X
DOI:10.5488/CMP.11.2.237