Canonical commutation relations and interacting Fock spaces
Ammari, Zied
Journées équations aux dérivées partielles, (2004), p. 1-13 / Harvested from Numdam
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We introduce by means of reproducing kernel theory and decomposition in orthogonal polynomials canonical correspondences between an interacting Fock space a reproducing kernel Hilbert space and a square integrable functions space w.r.t. a cylindrical measure. Using this correspondences we investigate the structure of the infinite dimensional canonical commutation relations. In particular we construct test functions spaces, distributions spaces and a quantization map which generalized the work of Krée-Rączka [KR] and Janas-Rudol [JR1]-[JR3].

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     author = {Ammari, Zied},
     title = {Canonical commutation relations and interacting Fock spaces},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2004},
     pages = {1-13},
     doi = {10.5802/jedp.2},
     zbl = {1067.35082},
     mrnumber = {2135357},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_2004____A2_0}
}

Ammari, Zied. Canonical commutation relations and interacting Fock spaces. Journées équations aux dérivées partielles,  (2004), pp. 1-13. doi : 10.5802/jedp.2. http://gdmltest.u-ga.fr/item/JEDP_2004____A2_0/

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