Quantum stochastic calculus and representations of Lie superalgebras
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| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1998
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| Schriftenreihe: | Lecture notes in mathematics
1692 |
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| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Eyre, Timothy M. W. |d 1971- |e Verfasser |0 (DE-588)12033612X |4 aut | |
| 245 | 1 | 0 | |a Quantum stochastic calculus and representations of Lie superalgebras |c Timothy M. W. Eyre |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1998 | |
| 300 | |a VIII, 138 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1692 | |
| 650 | 4 | |a Quantentheorie - Stochastischer Prozess - Stochastische Analysis - Lie-Superalgebra | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Quantum theory | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Stochastische Analysis |0 (DE-588)4132272-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantentheorie |0 (DE-588)4047992-4 |2 gnd |9 rswk-swf |
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| 689 | 0 | 2 | |a Stochastische Analysis |0 (DE-588)4132272-1 |D s |
| 689 | 0 | 3 | |a Lie-Superalgebra |0 (DE-588)4304027-5 |D s |
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Datensatz im Suchindex
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| _version_ | 1823052449028505600 |
| adam_text | 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 Z2 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 M0(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
5. The Ungraded Higher Order Ito Product Formula 51
5.1 The * Product 51
5.2 Fundamental Property of * 53
VIII Table of Contents
6. The Ito Superalgebra 59
6.1 Preliminary Definitions 59
6.2 Definition of the A»B 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 Zj Graded Quantum Stochastic Integrals 86
7.5 The Map I 89
7.6 Fundamental Property of * 90
7.7 The Injectivity of 7 96
7.8 The 0 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 M0(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
|
| any_adam_object | 1 |
| author | Eyre, Timothy M. W. 1971- |
| author_GND | (DE-588)12033612X |
| author_facet | Eyre, Timothy M. W. 1971- |
| author_role | aut |
| author_sort | Eyre, Timothy M. W. 1971- |
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| building | Verbundindex |
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| callnumber-subject | QA - Mathematics |
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| dewey-ones | 510 - Mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV012140344 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-03T16:57:40Z |
| institution | BVB |
| isbn | 3540648976 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008223198 |
| oclc_num | 246348605 |
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| owner_facet | DE-824 DE-91G DE-BY-TUM DE-739 DE-29 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | VIII, 138 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spellingShingle | Eyre, Timothy M. W. 1971- Quantum stochastic calculus and representations of Lie superalgebras Lecture notes in mathematics Quantentheorie - Stochastischer Prozess - Stochastische Analysis - Lie-Superalgebra Mathematische Physik Quantentheorie Mathematical physics Quantum theory Stochastic processes Stochastische Analysis (DE-588)4132272-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Quantentheorie (DE-588)4047992-4 gnd Lie-Superalgebra (DE-588)4304027-5 gnd |
| subject_GND | (DE-588)4132272-1 (DE-588)4057630-9 (DE-588)4047992-4 (DE-588)4304027-5 |
| title | Quantum stochastic calculus and representations of Lie superalgebras |
| title_auth | Quantum stochastic calculus and representations of Lie superalgebras |
| title_exact_search | Quantum stochastic calculus and representations of Lie superalgebras |
| title_full | Quantum stochastic calculus and representations of Lie superalgebras Timothy M. W. Eyre |
| title_fullStr | Quantum stochastic calculus and representations of Lie superalgebras Timothy M. W. Eyre |
| title_full_unstemmed | Quantum stochastic calculus and representations of Lie superalgebras Timothy M. W. Eyre |
| title_short | Quantum stochastic calculus and representations of Lie superalgebras |
| title_sort | quantum stochastic calculus and representations of lie superalgebras |
| topic | Quantentheorie - Stochastischer Prozess - Stochastische Analysis - Lie-Superalgebra Mathematische Physik Quantentheorie Mathematical physics Quantum theory Stochastic processes Stochastische Analysis (DE-588)4132272-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Quantentheorie (DE-588)4047992-4 gnd Lie-Superalgebra (DE-588)4304027-5 gnd |
| topic_facet | Quantentheorie - Stochastischer Prozess - Stochastische Analysis - Lie-Superalgebra Mathematische Physik Quantentheorie Mathematical physics Quantum theory Stochastic processes Stochastische Analysis Stochastischer Prozess Lie-Superalgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008223198&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT eyretimothymw quantumstochasticcalculusandrepresentationsofliesuperalgebras |