Analysis of Dirac systems and computational algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston u.a.
Birkhäuser
2004
|
| Schriftenreihe: | Progress in Mathematical Physics
39 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 332 S. |
| ISBN: | 0817642552 |
Internformat
MARC
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| 100 | 1 | |a Colombo, Fabrizio |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Analysis of Dirac systems and computational algebra |c Fabrizio Colombo ... |
| 264 | 1 | |a Boston u.a. |b Birkhäuser |c 2004 | |
| 300 | |a XIV, 332 S. | ||
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| 490 | 1 | |a Progress in Mathematical Physics |v 39 | |
| 650 | 4 | |a Analyse mathématique | |
| 650 | 7 | |a Análise matemática |2 larpcal | |
| 650 | 4 | |a Clifford, Algèbres de | |
| 650 | 4 | |a Dirac, Équation de | |
| 650 | 7 | |a Equações diferenciais parciais |2 larpcal | |
| 650 | 7 | |a Física matemática |2 larpcal | |
| 650 | 4 | |a Physique mathématique | |
| 650 | 7 | |a Álgebras de clifford |2 larpcal | |
| 650 | 4 | |a Équations aux dérivées partielles | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Clifford algebras | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Dirac equation | |
| 650 | 4 | |a Mathematical analysis | |
| 650 | 4 | |a Mathematical physics | |
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Datensatz im Suchindex
| _version_ | 1804132947615285248 |
|---|---|
| adam_text | Contents
Preface ix
1 Background Material 1
1.1 Algebraic tools 1
1.1.1 Commutative algebra 1
1.1.2 Gröbner bases: a quick introduction 11
1.1.3 Sheaftheory 23
1.2 Analytical tools 34
1.2.1 Topological linear spaces 34
1.2.2 Distributions 40
1.2.3 Fourier transform and fundamental Solutions 52
1.3 Elements of hyperfunction theory 60
1.3.1 Hyperfunctions in one variable 60
1.3.2 Cohomological properties of the sheaf of holomorphic
functions 74
1.3.3 Hyperfunctions of several variables 78
1.3.4 Fourier transform 85
1.4 Appendix: category theory 88
2 Computational Algebraic Analysis 93
2.1 A primer of algebraic analysis 93
2.2 The Ehrenpreis-Palamodov Fundamental Principle 116
2.3 The Fundamental Principle for hyperfunctions 126
2.4 Using computational algebra Software 131
viii Contents
3 The Cauchy-Fueter System and its Variations 139
3.1 Regulax functions of one quaternionic variable 139
3.2 Quaternionic hyperfunctions in one variable 148
3.3 Several quaternionic variables: an analytic approach 166
3.4 Several quaternionic variables: an algebraic approach 173
3.5 The Moisil-Theodorescu System 198
4 Special First Order Systems in Clifford Analysis 209
4.1 Introduction to Clifford algebras 209
4.1.1 Standard Clifford algebras 209
4.1.2 Endomorphisms and spinor Spaces 218
4.1.3 Classifications of real Clifford algebras 222
4.2 Introduction to Clifford analysis 225
4.2.1 Dirac Operators 225
4.2.2 Radial algebra 229
4.2.3 Fischer decomposition 231
4.3 The Dirac complex for two, three and four Operators 237
4.3.1 Case of two Operators 237
4.3.2 Case of three Operators 238
4.3.3 Case of four Operators 248
4.4 Special Systems in Clifford analysis 250
4.4.1 Generalized Systems 250
4.4.2 Systems using the Witt basis 253
4.4.3 Combinatorial Systems 262
5 Some First Order Linear Operators in Physics 267
5.1 Physics and algebra of Maxwell and Proca fields 270
5.2 Variations on Maxwell System in the space of biquaternions . . . 277
5.3 Properties of 2?z-regular functions 284
5.4 The Dirac equation and the linearization problem 293
5.5 Octonionic Dirac equation 296
6 Open Problems and Avenues for Further Research 307
6.1 The Cauchy-Fueter System 307
6.2 The Dirac System 308
6.3 Miscellanea 309
Bibliography 313
Index 327
|
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| indexdate | 2024-07-09T20:00:55Z |
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| isbn | 0817642552 |
| language | English |
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| physical | XIV, 332 S. |
| publishDate | 2004 |
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| publisher | Birkhäuser |
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| series | Progress in Mathematical Physics |
| series2 | Progress in Mathematical Physics |
| spelling | Colombo, Fabrizio Verfasser aut Analysis of Dirac systems and computational algebra Fabrizio Colombo ... Boston u.a. Birkhäuser 2004 XIV, 332 S. txt rdacontent n rdamedia nc rdacarrier Progress in Mathematical Physics 39 Analyse mathématique Análise matemática larpcal Clifford, Algèbres de Dirac, Équation de Equações diferenciais parciais larpcal Física matemática larpcal Physique mathématique Álgebras de clifford larpcal Équations aux dérivées partielles Mathematische Physik Clifford algebras Differential equations, Partial Dirac equation Mathematical analysis Mathematical physics Dirac-Operator (DE-588)4150118-4 gnd rswk-swf Clifford-Analysis (DE-588)4484012-3 gnd rswk-swf Clifford-Analysis (DE-588)4484012-3 s Dirac-Operator (DE-588)4150118-4 s DE-604 Progress in Mathematical Physics 39 (DE-604)BV013823265 39 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012925142&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Colombo, Fabrizio Analysis of Dirac systems and computational algebra Progress in Mathematical Physics Analyse mathématique Análise matemática larpcal Clifford, Algèbres de Dirac, Équation de Equações diferenciais parciais larpcal Física matemática larpcal Physique mathématique Álgebras de clifford larpcal Équations aux dérivées partielles Mathematische Physik Clifford algebras Differential equations, Partial Dirac equation Mathematical analysis Mathematical physics Dirac-Operator (DE-588)4150118-4 gnd Clifford-Analysis (DE-588)4484012-3 gnd |
| subject_GND | (DE-588)4150118-4 (DE-588)4484012-3 |
| title | Analysis of Dirac systems and computational algebra |
| title_auth | Analysis of Dirac systems and computational algebra |
| title_exact_search | Analysis of Dirac systems and computational algebra |
| title_full | Analysis of Dirac systems and computational algebra Fabrizio Colombo ... |
| title_fullStr | Analysis of Dirac systems and computational algebra Fabrizio Colombo ... |
| title_full_unstemmed | Analysis of Dirac systems and computational algebra Fabrizio Colombo ... |
| title_short | Analysis of Dirac systems and computational algebra |
| title_sort | analysis of dirac systems and computational algebra |
| topic | Analyse mathématique Análise matemática larpcal Clifford, Algèbres de Dirac, Équation de Equações diferenciais parciais larpcal Física matemática larpcal Physique mathématique Álgebras de clifford larpcal Équations aux dérivées partielles Mathematische Physik Clifford algebras Differential equations, Partial Dirac equation Mathematical analysis Mathematical physics Dirac-Operator (DE-588)4150118-4 gnd Clifford-Analysis (DE-588)4484012-3 gnd |
| topic_facet | Analyse mathématique Análise matemática Clifford, Algèbres de Dirac, Équation de Equações diferenciais parciais Física matemática Physique mathématique Álgebras de clifford Équations aux dérivées partielles Mathematische Physik Clifford algebras Differential equations, Partial Dirac equation Mathematical analysis Mathematical physics Dirac-Operator Clifford-Analysis |
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