Quantum Probability for Probabilists. 1st ed. 1993

種類:

電子ブック

責任表示:

by Paul-Andre Meyer

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1993

著者名:

• Meyer, Paul-Andre.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1538

ISBN:

9783662215586 [3662215586]    

注記:

I: Non Commutative Probability -- II: Spin -- III: The Harmonic Oscillator -- IV: Fock Space (1) -- V. Multiple Fock Spaces -- VI. Stochastic Calculus on Fock Space -- VII. Independence -- Appendix 1: Functional Analysis -- Hilbert-Schmidt operators (1) -- Trace class operators (2) -- Duality properties (3) Weak convergence properties (4) -- Weak topologies for operators (5) -- Tensor products of Hilbert spaces (6–7) -- Appendix 2: Conditioning and Kernels -- Conditioning: discrete case (1) -- Conditioning: continuous case (2) -- Example of the canonical pair (3) -- Multiplicity theory (4) -- Classical kernels (5) -- Non commutative kernels, first form (6) -- second form (7) -- Completely positive maps (8) -- Some difficulties (9) -- Appendix 3: Two Events -- 1. Elementary theory -- Application of spectral theory (2) -- Some elementary properties (3) -- Positive elements (4) -- Symbolic calculus for s.a. elements (5) -- Applications (6) -- Characterization of positive elements (7) -- A few inequalities (8) --
These notes contain all the material accumulated over six years in Strasbourg to teach "Quantum Probability" to myself and to an audience of commutative probabilists. The text, a first version of which appeared in successive volumes of the Seminaire de Probabilite8, has been augmented and carefully rewritten, and translated into international English. Still, it remains true "Lecture Notes" material, and I have resisted suggestions to publish it as a monograph. Being a non-specialist, it is important for me to keep the moderate right to error one has in lectures. The origin of the text also explains the addition "for probabilists" in the title : though much of the material is accessible to the general public, I did not care to redefine Brownian motion or the Ito integral. More precisely than "Quantum Probability" , the main topic is "Quantum Stochastic Calculus" , a field which has recently got official recognition as 81825 in the Math.

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