By Ouerdiane H., Barhoumi A. (eds.)
ISBN-10: 9814295426
ISBN-13: 9789814295420
This can be the complaints of the twenty ninth convention on Quantum chance and endless Dimensional research, which was once held in Hammamet, Tunisia.
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Additional info for Quantum Probability and Infinite Dimensional Analysis
Example text
Barhoumi, H. Ouerdiane & A. 1. The Lie algebra B generated by A† , A, N, I gives rise to a unitary equivalent irreducible representation of the L´evy-Meixner oscillator algebra A. Proof. From the relations (18) and (22) we read, for any n ≥ 0, [A† , A]Φn = λn λn+1 Φn − λn λn−1 = [ωn+1 − ωn ]Φn = [2βN + c2 I]Φn . In a similar way we found [N, A† ]Φn = A† Φn , [N, A]Φn = −AΦn . The irreducibility property is obvious from the completeness of the family {Φn }∞ n=0 in ΓLM . As it is expected, we want the Fock space representation of the L´evyMeixner oscillator to be unitary equivalent to the one in the L2 (µ)-space.
Math. ) 107 (1997), 223-235. 15. , Group representations in reproducing kernel Hilbert spaces, Report on Math. Physics 14 (1978), 247-259. 16. Chihara T. , An Introduction to orthogonal polynomials, Gordon and Breach, 1978. 17. , Partial differential equations in Fischer-Fock spaces for HilbertSchmidt holomorphy type, Bull. Amer. Math. Soc. 77 (1971), 725-730. 18. -P. R, Coherent states for systems with discrete and continuous spectrum, J. Phys. A: Math. Gen. 32 (1999), 123-136. 19. Glauber R.
0, ξ ⊗n , 0, . . ) → (0, . . , 0, nξ(t)ξ ⊗(n−1) , 0, . . ), ξ ∈ E. It is shown that at ∈ L((E), (E)). Its adjoint operator a∗t ∈ L((E)∗ , (E)∗ ) is called the creation operator at t. The pair {at , a∗t ; t ∈ T } is called the quantum white noise on T . , [9,19]. 2. Quantum white noise derivatives For f ∈ E ∗ we define white noise operators: f (t)at dt, a(f ) = Ξ0,1 (f ) = T a∗ (f ) = Ξ1,0 (f ) = T f (t)a∗t dt, (3) which are called respectively the annihilation and creation operators associated with f .
Quantum Probability and Infinite Dimensional Analysis by Ouerdiane H., Barhoumi A. (eds.)
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