Cargando…
Noncommutative mathematics for quantum systems /
"Discusses two current areas of noncommutative mathematics, quantum probability and quantum dynamical systems"--
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Cambridge University Press,
[2016]
|
| Colección: | Cambridge - IISc series.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Dedication; Contents; Preface; Conference photo; Introduction; 1 Independence and Lévy Processes in Quantum Probability; 1.1 Introduction; 1.2 What is Quantum Probability?; 1.2.1 Distinguishing features of classical and quantum probability; 1.2.2 Dictionary 'Classical ₄!Quantum'; 1.3 Why do we Need Quantum Probability?; 1.3.1 Mermin's version of the EPR experiment; 1.3.2 Gleason's theorem; 1.3.3 The Kochen-Specker theorem; 1.4 Infinite Divisibility in Classical Probability; 1.4.1 Stochastic independence; 1.4.2 Convolution.
- 1.4.3 Infinite divisibility, continuous convolution semigroups, and Lévy processes1.4.4 The De Finetti-Lévy-Khintchine formula on (R+, +); 1.4.5 Lévy-Khintchine formulae on cones; 1.4.6 The Lévy-Khintchine formula on (Rd, +); 1.4.7 The Markov semigroup of a Lévy process; 1.4.8 Hunt's formula; 1.5 Lévy Processes on Involutive Bialgebras.
- 1.5.1 Definition of Lévy processes on involutive bialgebras 1.5.2 The generating functional of a Lévy process ; 1.5.3 The Schürmann triple of a Lévy process; 1.5.4 Examples.
- 1.6 Lévy Processes on Compact Quantum Groups and their Markov Semigroups 1.6.1 Compact quantum groups; 1.6.2 Translation invariant Markov semigroups; 1.7 Independences and Convolutions in Noncommutative Probability; 1.7.1 Nevanlinna theory and Cauchy-Stieltjes transforms; 1.7.2 Free convolutions; 1.7.3 A useful Lemma; 1.7.4 Monotone convolutions.
- 1.7.5 Boolean convolutions1.8 The Five Universal Independences; 1.8.1 Algebraic probability spaces; 1.8.2 Classical stochastic independence and the product of probability spaces; 1.8.3 Products of algebraic probability spaces; 1.8.4 Classification of the universal independences; 1.9 Lévy Processes on Dual Groups ; 1.9.1 Dual groups.