.

0 (hodnocen0 x )

(1) Půjčeno:1x 

BK

Berlin : Springer, 1998

138 s.

ISBN 3-540-64897-6 (brož.)

Lecture notes in mathematics ; [vol.] 1692

Obsahuje úvod, rejstřík

Bibliografie: s. 133-134

Algebra Lieova - učebnice vysokošk.

Počet kvantitativní stochastický - učebnice vysokošk.

000087731

Table of Contents // 1. Introduction ... 1 // 1.1 Discussion ... 1 // 1.2 Overview ... 2 // 1.3 Notational Conventions ... 5 // 2. Quantum Stochastic Calculus ... 7 // 2.1 The Kernel Construction and Fock Space ... 7 // 2.2 The Processes of Quantum Stochastic Calculus ... 9 // 2.3 Construction of Simple Quantum Stochastic Integrals ... 12 // 2.4 Extending the Integral ... 15 // 2.5 Iterated Integrals ... 17 // 2.6 Boson-Fermion Unification ... 19 // 3. Z2-Graded Structures ... 23 // 3.1 Z2-Graded Vector Spaces ... 23 // 3.2 Z2-Graded Algebras ... 24 // 3.3 Lie Superalgebras ... 27 // 3.4 The Universal Enveloping Superalgebra ... 30 // 4. Representations of Lie Superalgebras in 22- Graded // Quantum Stochastic Calculus ... 33 // 4.1 Lie Algebra Representations in Ungraded Quantum // Stochastic Calculus ... 33 // 4.2 Boson-Fermion Equivalence in Quantum Stochastic // Calculus of Dimension 1 ... 34 // 4.3 A Partial Generalisation ... 37 // 4.4 The Construction of N, r) ... 38 // 4.5 Definition of the Processes of Z2-Graded Quantum // Stochastic Calculus ... 41 // 4.6 Some Lemmas ... 43 // 4.7 The Main Theorem ... 47 // The Ungraded Higher Order Ito Product Formula // 51 // 5.1 The * Product ... 51 // 5.2 Fundamental Property of * ... 53 // VIII Table of Contents // The Ito Superalgebra // 59 // 6.1 Preliminary Definitions ... 59 // 6.2 Definition of the A9B Products ... 61 // 6.3 A Computational Device ... 62 // 6.4 The � Product ... 64 // 6.5 Supersymmetric Tensors ... 66

// 7. Some Results in Z2-Graded Quantum Stochastic // Calculus ... 77 // 7.1 The First Fundamental Formula in Z2-Graded Quantum // Stochastic Calculus ... 77 // 7.2 The Second Fundamental Formula in Z2-Graded Quantum // Stochastic Calculus ... 78 // 7.3 Discussion of the Second Fundamental Formula in // Z2-Graded Quantum Stochastic Calculus ... 80 // 7.4 Adjoints of Z2-Graded Quantum Stochastic Integrals ... 86 // 7.5 The Map 1 ... 89 // 7.6 Fundamental Property of � ... 90 // 7.7 The Injectivity of Z ... 96 // 7.8 The G Product ... 98 // 8. Chaotic Expansions ... 101 // 8.1 Preliminaries ... 101 // 8.2 The Co-Unit ... 102 // 8.3 The Co-Product and the Difference Map K ... 106 // 8.4 The Chaos Map ... 108 // 9. Extensions ... 113 // 9.1 Introduction ... 113 // 9.2 Zn-Grading of Mo(N) ... 113 // 9.3 Zn-Grading of Quantum Stochastic Calculus ... 115 // 9.4 Conjugation ... 116 // 9.5 The Taking of Adjoints ... 119 // 9.6 The Second Fundamental Formula in Zn-Graded Quantum // Stochastic Calculus ... 122 // 9.7 The Higher Order Ito Product Formula in Zn-Graded // Quantum Stochastic Calculus ... 124 // 9.8 Commutation Relations ... 125 // 9.9 Alternative Sources of Commutation Relations ... 125 // 9.10 Zn-Graded Quantum Stochastic Calculus With Infinite // Degrees of Freedom ... 129 // References // 133 // Index ... // 135