×

Exchange operators and some applications of the kernel methods. (Opérateurs d’échange et quelques applications des méthodes de noyaux.) (French) Zbl 0773.60060

A question posed by P. A. Meyer on calculating the law of an operator- valued process involving creation and annihilation on the Fock space on \(L^ 2[0,1]\times L^ 2[0,1]\) is answered in this paper.

MSC:

60H99 Stochastic analysis
81S25 Quantum stochastic calculus
PDF BibTeX XML Cite
Full Text: Numdam EuDML

References:

[1] Berezin F.A. - The method of second quantization . Academic Press , 1966 . MR 208930 | Zbl 0151.44001 · Zbl 0151.44001
[2] Dermoune A. - Quelques interactions entre le calcul stochastique et les probabilités non commutatives , Manuscrit 1989 .
[3] Emery M. - On the Azema martingale , à paraître. Numdam · Zbl 0753.60045
[4] Krée P. , Raczka R. - Kernel and symbol in quantum field theory . Ann. Inst. H.Poincaré , section A, vol. 28 , n^\circ 1 , pp. 41 - 73 , 1978 . Numdam | MR 482179 | Zbl 0386.47015 · Zbl 0386.47015
[5] Krée P. - Dim. Free stochastic calculus in the distribution sens , à paraître. · Zbl 0682.46028
[6] Meyer P.A. - I.s.m. par rapport à certaines martingales . Séminaire de probabilité , X , pp. 325 - 331 .
[7] Meyer P.A. - Eléments de probabilités quantiques . Séminaire de probabilité , XX . Numdam
[8] Meyer P.A. - Probabilités non commutatives sur l’espace de Fock , à paraître, 1989 .
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.