Quantum Probability for Probabilists (Record no. 31327)

000 -LEADER
fixed length control field 05421nam a22005175i 4500
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 9783662215586
-- 978-3-662-21558-6
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 519.2
100 1# - MAIN ENTRY--AUTHOR NAME
Personal name Meyer, Paul-André.
245 10 - TITLE STATEMENT
Title Quantum Probability for Probabilists
Statement of responsibility, etc by Paul-André Meyer.
260 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication Berlin, Heidelberg :
Name of publisher Springer Berlin Heidelberg :
-- Imprint: Springer,
Year of publication 1993.
300 ## - PHYSICAL DESCRIPTION
Number of Pages X, 293 p.
Other physical details online resource.
490 1# - SERIES STATEMENT
Series statement Lecture Notes in Mathematics, Institut de Mathématiques, Université de Strasbourg,
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note 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) -- Existence of many states (1) -- Representations and the GNS theorem (2–3) -- Examples from toy Fock space theory (4) -- Quotient algebras and approximate units (5) -- 3. Von Neumann algebras -- Weak topologies and normal states (1) -- Von Neumann’s bicommutant theorem (2–3) -- Kaplanski’s density theorem (4) -- The predual (5) -- Normality and order continuity (6) -- About integration theory (7) -- Measures with bounded density (8) -- The linear Radon-Nikodym theorem (9) -- The KMS condition (10) -- Entire vectors (11) -- 4. The Tomita-Takesaki theory -- Elementary geometric properties (1) -- The main operators (2–3) -- Interpretation of the adjoint (4) -- The modular property (5) -- Using the linear RN theorem (6) -- The main computation (7) -- The three main theorems (8) -- Additional results (9) -- Examples (10) -- Appendix 5: Local Times and Fock Space -- 1. Dynkin’s formula -- Symmetric Markov semigroups and processes (1) -- Dynkin’s formula (2) -- Sketch of the Marcus-Rosen approach to the continuity of local times (3) -- 2. Le Jan’s “supersymmetric” approach -- Notations of complex Brownian motion (1) -- Computing the Wiener product (2) -- Stratonovich integral and trace (4) -- Expectation of the exponential of an element of the second chaos (5) -- Exponential formula in the antisymmetric case (7) -- Supersymmetric Fock space: the Wick and Wiener products (8) -- Properties of the Wiener product (9) -- Applications to local times (sketch) (10) -- References -- Index of Notation.
520 ## - SUMMARY, ETC.
Summary, etc 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.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Mathematics.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Distribution (Probability theory).
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Mathematics.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Probability Theory and Stochastic Processes.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Theoretical, Mathematical and Computational Physics.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Laser Technology, Photonics.
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Quantum Optics.
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier http://dx.doi.org/10.1007/978-3-662-21558-6
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type E-BOOKS
264 #1 -
-- Berlin, Heidelberg :
-- Springer Berlin Heidelberg :
-- Imprint: Springer,
-- 1993.
336 ## -
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-- txt
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-- computer
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-- rdamedia
338 ## -
-- online resource
-- cr
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347 ## -
-- text file
-- PDF
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830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
-- 0075-8434 ;
Holdings
Withdrawn status Lost status Damaged status Not for loan Current library Accession Number Uniform Resource Identifier Koha item type
        IMSc Library EBK2033 http://dx.doi.org/10.1007/978-3-662-21558-6 E-BOOKS
The Institute of Mathematical Sciences, Chennai, India

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