Spectral analysis of relativistic operators:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
London
Imperial College Press
2011
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Angekündigt als: Spectral theory of relativistic operators |
| Physical Description: | XII, 186 S. |
| ISBN: | 9781848162181 1848162189 |
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| 100 | 1 | |a Balinsky, Alexander A. |e Verfasser |0 (DE-588)143306162 |4 aut | |
| 245 | 1 | 0 | |a Spectral analysis of relativistic operators |c A. A. Balinsky and W. D. Evans |
| 246 | 1 | 3 | |a Spectral theory of relativistic operators |
| 264 | 1 | |a London |b Imperial College Press |c 2011 | |
| 300 | |a XII, 186 S. | ||
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Record in the Search Index
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| adam_text | Titel: Spectral analysis of relativistic operators
Autor: Balinsky, Alexander A
Jahr: 2011
Contents
Preface vii
1. Preliminaries 1
1.1 Linear Operators............................ 1
1.2 Quadratic forms ............................ 3
1.3 Spectra of self-adjoint Operators.................... 7
1.4 Compact Operators........................... 8
1.5 Fourier and Mellin transforms..................... 9
1.6 Sobolev Spaces............................. 15
1.7 Inequalities............................... 17
1.8 CLR and related inequalities..................... 20
1.8.1 The Schrödinger Operator................... 23
1.8.2 The magnetic Schrödinger Operator............. 23
1.8.3 The quasi-relativistic Schrödinger Operator......... 23
1.8.4 The magnetic quasi-relativistic Schrödinger Operator ... 24
1.9 Lieb-Thirring inequalities....................... 25
2. Operators 27
2.1 The Dirac Operator........................... 27
2.1.1 Partial wave decomposition.................. 29
2.1.2 Spherically Symmetrie electric potentials.......... 34
2.1.3 Matrix-valued potentials................... 41
2.2 The quasi-relativistic Operator..................... 46
2.2.1 The Kato inequality...................... 47
2.2.2 The self-adjoint realisation.................. 53
2.2.3 The ränge 1/2 7 2/7r for h0............... 57
2.3 The Brown-Ravenhall Operator.................... 62
2.3.1 Coulomb potentials...................... 64
2.3.2 Lower semi-boundedness................... 67
2.3.3 The Brown-Ravenhall Operators b/,s ............ 77
xii Spectral Analysis of Relativistic Operators
2.4 A unique continuation property.................... 81
3. Spectra 85
3.1 The Dirac Operator........................... 85
3.1.1 Preliminary lemmas...................... 85
3.1.2 The essential spectrum of H3 ................. 87
3.1.3 Eigenvalues in (-1,1)..................... 88
3.1.4 Min-max characterisation................... 92
3.2 The quasi-relativistic Operator..................... 92
3.2.1 The essential spectrum.................... 92
3.3 The Brown-Ravenhall Operator.................... 95
3.3.1 The essential spectrum.................... 95
3.3.2 The virial theorem....................... 96
3.4 The absence of embedded eigenvalues ................ 101
4. Miscellany 109
4.1 Stability of matter........................... 109
4.2 Eigenvalues of the Operators Da and Pa............... H3
4.2.1 Examples of zero modes.................... 113
4.2.2 Chern-Simons actions for magnetic fields with zero
modes.............................. 120
4.2.3 Quaternionic description of zero modes........... 121
4.3 Zero modes of DA and PA in Rn, n 2................ 126
4.4 Decay rates of weak Solutions of B Qip = 0.............. 133
4.4.1 Reduction by inversion.................... 134
4.4.2 Embeddings of Dirac-Sobolev spaces............ 136
4.4.3 Decay of zero modes...................... 141
4.5 Sobolev and CLR inequalities for Pauli Operators.......... 142
4.6 One-electron relativistic molecules.................. 149
4.6.1 Quasi-relativistic model.................... 149
4.6.2 The Brown-Ravenhall model................. 153
4.7 Stability of matter in magnetic fields................. 168
4.7.1 Non-relativistic matter.................... 169
4.7.2 Relativistic matter....................... 173
Bibliography 177
Index 183
List of Symbols 185
|
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| author | Balinsky, Alexander A. Evans, W. D. 1940- |
| author_GND | (DE-588)143306162 (DE-588)129315184 |
| author_facet | Balinsky, Alexander A. Evans, W. D. 1940- |
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| id | DE-604.BV036955374 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:51:28Z |
| institution | BVB |
| isbn | 9781848162181 1848162189 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020870365 |
| oclc_num | 706967247 |
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| owner_facet | DE-355 DE-BY-UBR DE-824 DE-19 DE-BY-UBM DE-11 |
| physical | XII, 186 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Imperial College Press |
| record_format | marc |
| spelling | Balinsky, Alexander A. Verfasser (DE-588)143306162 aut Spectral analysis of relativistic operators A. A. Balinsky and W. D. Evans Spectral theory of relativistic operators London Imperial College Press 2011 XII, 186 S. txt rdacontent n rdamedia nc rdacarrier Angekündigt als: Spectral theory of relativistic operators Operator theory Spectral theory (Mathematics) Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s Spektraltheorie (DE-588)4116561-5 s DE-604 Evans, W. D. 1940- Verfasser (DE-588)129315184 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020870365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Balinsky, Alexander A. Evans, W. D. 1940- Spectral analysis of relativistic operators Operator theory Spectral theory (Mathematics) Spektraltheorie (DE-588)4116561-5 gnd Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4075665-8 |
| title | Spectral analysis of relativistic operators |
| title_alt | Spectral theory of relativistic operators |
| title_auth | Spectral analysis of relativistic operators |
| title_exact_search | Spectral analysis of relativistic operators |
| title_full | Spectral analysis of relativistic operators A. A. Balinsky and W. D. Evans |
| title_fullStr | Spectral analysis of relativistic operators A. A. Balinsky and W. D. Evans |
| title_full_unstemmed | Spectral analysis of relativistic operators A. A. Balinsky and W. D. Evans |
| title_short | Spectral analysis of relativistic operators |
| title_sort | spectral analysis of relativistic operators |
| topic | Operator theory Spectral theory (Mathematics) Spektraltheorie (DE-588)4116561-5 gnd Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Operator theory Spectral theory (Mathematics) Spektraltheorie Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020870365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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