De Sitter invariant special relativity:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2015
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XIV, 265 S. graph. Darst. |
| ISBN: | 9814618705 9789814618700 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804175171862396928 |
|---|---|
| adam_text | De Sitter Invariant Special Relativity
Einstein s Special Relativity (E-SR) is one of the cornerstones of modern physics. When the Einstein s cosmological constant A is non-zero in spacetime, E-SR will naturally become De Sitter Invariant SR (dS/AdS-SR). Hence it is essentially related to the foundation of physics. This book provides a description of dS/AdS-SR in terms of Lagrangian-Hamiltonian formulation with spacetime metric of inertial reference frames.
One of the outstanding features of the book is that all descriptions of SR are in the inertial reference frames. This is a requirement due to the first principle of SR theory. The descriptions of dS/AdS-SR in this book satisfy this principle. It is highly non-trivial for the curved spacetime in dS/AdS-SR theory.
Contents
ft
Preface • vii
1. General Introduction 1
2. Overview of Einstein’s Special Relativity (E-SR) 9
2.1 Inertial system of reference and relativity principle .... 9
2.2 Lorentz transformation and Minkowski spacetime............. 10
2.3 Landau-Lifshitz action and relativistic mechanics.......... 12
2.4 Canonical formulism of E-SR mechanics...................... 14
2.5 Noether’s theorem and the motion integrals................. 15
2.6 Noether charges of E-SR mechanics.......................... 19
2.7 Quantization of E-SR mechanics............................. 23
2.8 Localization of E-SR spacetime symmetry and Einstein’s
General Relativity (I) ....................... 25
2.9 Localization of E-SR spacetime symmetry and Einstein’s
General Relativity (II).................................... 37
3. De Sitter Invariant Special Relativity 43
3.1 Beltrami metrics........................................... 43
3.2 Motion of a particle in the Beltrami spacetime............. 45
3.3 Lagrangian mechanics of free particles in the Beltrami
spacetime.................................................. 48
3.4 Spacetime transformation preserving Beltrami metric ... 51
3.5 Noether charges of dS-SR mechanics......................... 57
XI
xii De Sitter Invariant Special Relativity
3.6 Hamilton and canonical momenta............................ 63
3.7 Dispersion relation....................................... 68
3.8 Minkowski point in Beltrami spacetime .................... 70
4. De Sitter Invariant General Relativity 73
4.1 Localization of Lu-Zou-Guo transformation and action of
de Sitter invariant General Relativity................... 74
4.2 Static spherically symmetric solution in empty spacetime 76
4.3 Beltrami-de Sitter-Schwarzschild Solution................. 79
5. Dynamics of Expansion of the Universe in General Relativity 87
5.1 Robertson-Walker metric................................... 88
5.2 Friedmann equation........................................ 91
5.3 The Friedmann models...................................... 95
5.4 ACDM model................................................ 97
5.5 Accelerated expansion.................................... 103
5.6 Cosmological constant.................................... 104
6. Relativistic Quantum Mechanics for de Sitter Invariant
Special Relativity 107
6.1 Quantization of the de Sitter invariant special relativistic
mechanics............................................... 107
6.2 Dirac equation in Beltrami spacetime .................... 110
6.2.1 Introduction..................................... 110
6.2.2 Weyhs approach................................. Ill
6.2.3 Dirac equation in Beltrami spacetime............. 114
7. Distant Hydrogen Atom in Cosmology 119
7.1 Introduction............................................. 119
7.2 Beltrami local inertial coordinate system in light cone of
Ricci Friedmann-Robertson—Walker universe............... 122
7.3 Hydrogen atom at distant locally inertial coordinate
system in light cone of RFW universe................... 126
7.4 Solutions of ordinary Einstein relativistic Dirac
equation for Hydrogen atom at QSO....................... 127
Contents xiii
7.4.1 Eigenvalues and eigenstates....................... 127
7.4.2 2s1/2 and 2p1/2 states of Hydrogen.............. . 130
7.5 De Sitter invariant relativistic Dirac equation for
distant Hydrogen atom...................................... 132
7.6 De Sitter relativistic quantum mechanics spectrum
equation for Hydrogen .................................... 136
7.7 Adiabatic approximation solution to de Sitter—Dirac
spectra equation and time variation of physical constants.................................................. 139
7.8 2s1 /2-2p1 /2 splitting in the dS-SR Dirac equation of
Hydrogen................................................... 142
7.8.1 Energy levels shifts of Hydrogen in dS-SR QM as perturbation effects of E-SR Dirac equation of
atom............................................... 142
7.8.2 2s1/2 - 2px/2 splitting caused by H ............... 145
7.9 High-order calculations of l/R2-expansions............. 150
7.10 Universal constant variations over cosmological time . . . 154
8. Temporal and Spatial Variation of the Fine Structure Constant 157
8.1 Methods to search for changes of fine-structure constant . 157
8.2 Spacetime variations of fine-structure constant estimated
via combining Keck /HIRES- and VLT /UVES-observation data....................................................... 160
8.3 An overview of implication of spacetime variations of fine-
structure constant......................................... 163
8.4 Light-cone of Ricci Friedmann—Robertson—Walker universe 169
8.5 Local inertial coordinate system in light-cone of RFW
universe with Einstein cosmology constant.................. 171
8.6 Electric Coulomb law at light-cone of RFW universe . . . 177
8.7 Fine structure constant variation in {Q°, Q1, 0, 0} . . . . 181
8.7.1 Formulation of alpha-variation for case of © = 7r,
and 0.......................................... 182
8.7.2 Comparisons with observations of alpha-varying
for cases of © = 0, re ............................ 190
8.8 a-Varying in whole sky .................................... 193
xiv De Sitter Invariant Special Relativity
8*9 Summary and comments....................................... 196
9. De Sitter Invariance of Generally Covariant Dirac Equation 201
9.1 Giirsey-Lee metric of de Sitter spacetime.................. 201
9.2 Proof of Eq.(9.21) . . . . -.............................. 209
9.3 de Sitter invariance....................................... 210
Appendix A Solutions of Dirac Equation of Hydrogen in
Minkowski Spacetime 213
A.l Pauli equation in a central potential...................... 213
A.2 Relativistic quantum numbers and spin-angular functions 218
A.3 Dirac equation for Hydrogen ............................... 220
A. 4 Explicit wave functions for one-electron atom with
principal quantum number n = 1 and 2 227
A.5 Mathematica calculation for practice....................... 228
Appendix B The Confluent Hypergeo metric Function 231
Appendix C Spherical Harmonics 233
Appendix D Electric Coulomb Law in QSO-Light-Cone Space 235
Appendix E Adiabatic Approximative Wave Functions in
vacde Sitter-Dirac Equation of Hydrogen 239
Appendix F Matrix Elements of H in (2s1/ 2-2p1//2)-
Hilbert Space 243
Appendix G Solutions of Exercises 249
Bibliography 259
Index
263
|
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| id | DE-604.BV042885135 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:12:03Z |
| institution | BVB |
| isbn | 9814618705 9789814618700 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028313856 |
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| owner | DE-703 DE-19 DE-BY-UBM |
| owner_facet | DE-703 DE-19 DE-BY-UBM |
| physical | XIV, 265 S. graph. Darst. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Yan, Mu-Lin 1941- Verfasser (DE-588)1076831893 aut De Sitter invariant special relativity Mu-Lin Yan Singapore [u.a.] World Scientific 2015 XIV, 265 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De-Sitter-Kosmos (DE-588)4373790-0 gnd rswk-swf Spezielle Relativitätstheorie (DE-588)4182215-8 gnd rswk-swf De-Sitter-Kosmos (DE-588)4373790-0 s Spezielle Relativitätstheorie (DE-588)4182215-8 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028313856&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028313856&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Yan, Mu-Lin 1941- De Sitter invariant special relativity De-Sitter-Kosmos (DE-588)4373790-0 gnd Spezielle Relativitätstheorie (DE-588)4182215-8 gnd |
| subject_GND | (DE-588)4373790-0 (DE-588)4182215-8 |
| title | De Sitter invariant special relativity |
| title_auth | De Sitter invariant special relativity |
| title_exact_search | De Sitter invariant special relativity |
| title_full | De Sitter invariant special relativity Mu-Lin Yan |
| title_fullStr | De Sitter invariant special relativity Mu-Lin Yan |
| title_full_unstemmed | De Sitter invariant special relativity Mu-Lin Yan |
| title_short | De Sitter invariant special relativity |
| title_sort | de sitter invariant special relativity |
| topic | De-Sitter-Kosmos (DE-588)4373790-0 gnd Spezielle Relativitätstheorie (DE-588)4182215-8 gnd |
| topic_facet | De-Sitter-Kosmos Spezielle Relativitätstheorie |
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