Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-24T10:25:50.023Z Has data issue: false hasContentIssue false
  • English
  • Français

On the interacting Free Fock space and the deformed Wigner law

Published online by Cambridge University Press:  22 January 2016

Y. G. Lu
Y. G. Lu*
Affiliation:
Universitá degli studi di Ban Dipartimento di Mate, Campus Universitario, Via E. Orabona 4 70125 Bari, Italy
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Fock space is a basic structure for the quantum field theory and quantum stochastic calculus. In all the cases, a Fock space can be described as a direct sum of a sequence of some Hilbert spaces, i.e. a Fock space has the form of , where, is the complex field and is a given Hilbert space.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 145 , March 1997 , pp. 1 - 28
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1997

References

[ 1 ] Accardi, L., Lu, Y. G., Wiener noise versus Wigner noise in quantum electrodynamics, Q-P-R-T, YIII (1993), 1–18.Google Scholar
[ 2 ] Accardi, L., Lu, Y. G., Quantum electrodynamics and semi-circle noise, to appear in: International Journal of Nonlinear Physics.Google Scholar
[ 3 ] Lu, Y.G., Interacting Boson Fock space, submitted to Sci. Sin (A).Google Scholar
[ 4 ] Lu, Y.G., Quantum Stochastic Calculus on the Interacting Free Fock Space, submitted to J. Funct. Anal.Google Scholar
[ 5 ] Lu, Y.G., Some remarks on the deformed Wigner law, in preparation.Google Scholar
[ 6 ] Wigner, E., Characteristic vectors of bordered matrices with infinite dimension, Ann of Math., 62 (1955), 548–564.CrossRefGoogle Scholar
[ 7 ] Wigner, E., On the distribution of the roots of certain symmetric matrices, Ann of Math., 67(1958), 325–327.Google Scholar
[ 8 ] Voiculescu, D., Free noncommutative random variables, random matrices and the II1 factors of free groups, Q-P-R-T, VI (1991), 473–487.Google Scholar
[ 9 ] Voiculescu, D., Symmetries of some reduced free product C -algebras, Lect. Notes. Math., no. 1132 (1983), 556–588.Google Scholar
[10] Kümmerer, B., Speicher, R., Stochastic integration on the Curtz algebra 0∞. J. Funct. Anal. 103, no. 2 (1992), 372–408.CrossRefGoogle Scholar
[11] Speicher, R., A new example of “independence” and “white noise”. Proba. Th. Rel. Fields. 84 (1990), 141–159.Google Scholar
[12] Speicher, R., Survey on the stochastic integration on the full Fock space. Q-P-R-T VI (1991), 421–436.Google Scholar
[13] Fagnola, F., On quantum stochastic integration with respect to “free” noises. Q-P-R-T VI (1991), 285–304.Google Scholar
[14] Lu, Y.G., A note on free stochastic calculus on Hilbert modules, submitted to: Random operators.Google Scholar
[15] DeGiosa, M., Lu, Y. G., The free creation and annihilation operators as the central limit of quantum Bernoulli process, submitted to Ran. Op. Sto. Eq.Google Scholar
[16] DeGiosa, M., Lu, Y. G., From quantum Bernoulli process to creation and annihilation operators on interacting #-Fock space, submitted to Nagoya Math. J.Google Scholar
[17] DeGiosa, M., Lu, Y. G., The passage from 2 × 2 matrices model to an interacting free Fock space, preprint.Google Scholar
[18] Lu, Y.G., An Interacting Free Fock Space and the reciprocal-Wigner Law, to appear in Proba. Th. Math. Stat. (1997).Google Scholar
[19] Lu, Y.G., On the Anderson Type Interacting Free Fock Space, submitted to Ann. Proba.Google Scholar
[20] Lu, Y.G., Ruggeri, S., A new example of interacting Fock space and the distribution of field operator, submitted to Bollettino U. M. I.Google Scholar