Canonical commutation relations and interacting Fock spaces

Zied Ammari[1]

  • [1] Université Cergy-Pontoise Site Saint Martin 95302 Cergy-Pontoise cedex

Journées Équations aux dérivées partielles (2004)

  • page 1-13
  • ISSN: 0752-0360

Abstract

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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].

How to cite

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Ammari, Zied. "Canonical commutation relations and interacting Fock spaces." Journées Équations aux dérivées partielles (2004): 1-13. <http://eudml.org/doc/10594>.

@article{Ammari2004,
abstract = {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].},
affiliation = {Université Cergy-Pontoise Site Saint Martin 95302 Cergy-Pontoise cedex},
author = {Ammari, Zied},
journal = {Journées Équations aux dérivées partielles},
keywords = {Schrödinger equation; commutation relations; reproducing kernel Hilbert space; quantization map},
language = {eng},
month = {6},
pages = {1-13},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Canonical commutation relations and interacting Fock spaces},
url = {http://eudml.org/doc/10594},
year = {2004},
}

TY - JOUR
AU - Ammari, Zied
TI - Canonical commutation relations and interacting Fock spaces
JO - Journées Équations aux dérivées partielles
DA - 2004/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 13
AB - 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].
LA - eng
KW - Schrödinger equation; commutation relations; reproducing kernel Hilbert space; quantization map
UR - http://eudml.org/doc/10594
ER -

References

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  10. Baez, J. C., Segal, I. E., Zhou, Z.F., Introduction to algebraic and constructive quantum field theory, Princeton Series in Physics, Princeton University Press, (1992) Zbl0760.46061MR1178936
  11. Dunkl, C., Xu, Y.: Orthogonal Polynomials of Several Variables, Encyclopedia of Mathematics and its Applications, vol. 81, Cambridge Univ. Press, 2001. Zbl0964.33001MR1827871
  12. Janas, J., Rudol, K.: Toeplitz operators on the Segal-Bargmann space of infinitely many variables, Linear operators in function spaces (Timişoara, 1988), Oper. Theory Adv. Appl., 43, 217-228, Birkhäuser Zbl0705.47024MR1090129
  13. Janas, J., Rudol, K., Toeplitz operators in infinitely many variables, Topics in operator theory, operator algebras and applications (Timişoara, 1994), 147-160, Rom. Acad., Bucharest, 1995 Zbl0866.47016MR1421121
  14. Janas, J., Rudol, K.: Two approaches to Toeplitz operators on Fock space, Quantization and infinite-dimensional systems (Bialowieza, 1993), 3-7, Plenum Zbl0980.47500MR1377967
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