Geometric algebra and applications to physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Taylor & Francis
2007
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Inhaltsverzeichnis |
| Beschreibung: | 168 S. graph. Darst. |
| ISBN: | 1584887729 9781584887720 |
Internformat
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| 245 | 1 | 0 | |a Geometric algebra and applications to physics |c Venzo de Sabbata and Bidyut Kumar Datta |
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| adam_text | GEOMETRIC ALGEBRA AND APPLICATIONS TO PHYSICS VENZO DE SABBATA BIDYUT
KUMAR DATTA TAYLOR &. FRANCIS TAYLOR & FRANCIS CROUP NEW YORK LONDON
TAYLOR & FRANCIS IS AN IMPRINT OF THE TAYLOR & FRANCIS CROUP, AN INFORMA
BUSINESS CONTENTS PART 1 1 1 THE BASIS FOR GEOMETRIC ALGEBRA 3 1.1
INTRODUCTION 3 1.2 GENESIS OF GEOMETRIC ALGEBRA 4 1.3 MATHEMATICAL
ELEMENTS OF GEOMETRIC ALGEBRA 10 1.4 GEOMETRIC ALGEBRA AS A SYMBOLIC
SYSTEM 13 1.5 GEOMETRIC ALGEBRA AS AN AXIOMATIC SYSTEM (AXIOM A) 18 1.6
SOME ESSENTIAL FORMULAS AND DEFINITIONS 23 REFERENCES 26 2 MULTIVECTORS
27 2.1 GEOMETRIC PRODUCT OF TWO BIVECTORS A AND B 27 2.2 OPERATION OF
REVERSION 29 2.3 MAGNITUDE OF A MULTIVECTOR 30 2.4 DIRECTIONS AND
PROJECTIONS 30 2.5 ANGLES AND EXPONENTIAL FUNCTIONS (AS OPERATORS) 34
2.6 EXPONENTIAL FUNCTIONS OF MULTIVECTORS 37 REFERENCES 39 3 EUCLIDEAN
PLANE 41 3.1 THE ALGEBRA OF EUCLIDEAN PLANE 41 3.2 GEOMETRIC
INTERPRETATION OF A BIVECTOR OF EUCLIDEAN PLANE 44 3.3 SPINOR /-PLANE 45
3.3.1 CORRESPONDENCE BETWEEN THE /-PLANE OF VECTORS AND THE SPINOR PLANE
47 3.4 DISTINCTION BETWEEN VECTOR AND SPINOR PLANES 47 3.4.1 SOME
OBSERVATIONS 49 3.5 THE GEOMETRIC ALGEBRA OF A PLANE 50 REFERENCES 51 4
THE PSEUDOSCALAR AND IMAGINARY UNIT 53 4.1 THE GEOMETRIC ALGEBRA OF
EUCLIDEAN 3-SPACE 53 4.1.1 THE PSEUDOSCALAR OF E 3 56 4.2 COMPLEX
CONJUGATION 57 APPENDIX A: SOME IMPORTANT RESULTS 57 REFERENCES 58 5
REAL DIRAC ALGEBRA :. 59 5.1 GEOMETRIC SIGNIFICANCE OF THE DIRAC
MATRICES Y M 59 5.2 GEOMETRIC ALGEBRA OF SPACE-TIME 60 5.3 CONJUGATIONS
64 5.3.1 CONJUGATE MULTIVECTORS (REVERSION) 64 5.3.2 SPACE-TIME
CONJUGATION 65 5.3.3 SPACE CONJUGATION 65 5.3.4 HERMITIAN CONJUGATION 65
5.4 LORENTZ ROTATIONS 66 5.5 SPINOR THEORY OF ROTATIONS IN
THREE-DIMENSIONAL EUCLIDEAN SPACE 69 REFERENCES 72 6 SPINOR AND
QUATERNION ALGEBRA 75 6.1 SPINOR ALGEBRA: QUATERNION ALGEBRA 75 6.2
VECTOR ALGEBRA 77 6.3 CLIFFORD ALGEBRA: GRAND SYNTHESIS OF ALGEBRA OF
GRASSMANN AND HAMILTON AND THE GEOMETRIC ALGEBRA OF HESTENES 78
REFERENCES 80 PART II 81 7 MAXWELL EQUATIONS 83 7.1 MAXWELL EQUATIONS IN
MINKOWSM SPACE-TIME 83 7.2 MAXWELL EQUATIONS IN RIEMANN SPACE-TIME (V4
MANIFOLD) 85 7.3 MAXWELL EQUATIONS IN RIEMANN-CARTAN SPACE-TIME (U4
MANIFOLD) 86 7.4 MAXWELL EQUATIONS IN TERMS OF SPACE-TIME ALGEBRA (STA)
88 REFERENCES 91 8 ELECTROMAGNETIC FIELD IN SPACE AND TIME (POLARIZATION
OF ELECTROMAGNETIC WAVES) 93 8.1 ELECTROMAGNETIC (E.M.) WAVES AND
GEOMETRIC ALGEBRA 93 8.2 POLARIZATION OF ELECTROMAGNETIC WAVES 94 8.3
QUATERNION FORM OF MAXWELL EQUATIONS FROM THE SPINOR FORM OF STA 97 8.4
MAXWELL EQUATIONS IN VECTOR ALGEBRA FROM THE QUATERNION (SPINOR)
FORMALISM 99 8.5 MAJORANA-WEYL EQUATIONS FROM THE QUATERNION (SPINOR)
FORMALISM OF MAXWELL EQUATIONS 100 APPENDIX A: COMPLEX NUMBERS IN
ELECTRODYNAMICS 103 APPENDIX B: PLANE-WAVE SOLUTIONS TO MAXWELL
EQUATIONS * POLARIZATION OF E.M. WAVES 105 REFERENCES 107 9 GENERAL
OBSERVATIONS AND GENERATORS OF ROTATIONS (NEUTRON INTERFEROMETER
EXPERIMENT) 109 9.1 REVIEW OF SPACE-TIME ALGEBRA (STA) 109 9.1.1 NOTE
110 9.1.2 MULTIVECTORS ILL 9.1.3 REVERSION ILL 9.1.4 LORENTZ ROTATION K
ILL 9.1.5 TWO SPECIAL CLASSES OF LORENTZ ROTATIONS: BOOSTS AND SPATIAL
ROTATIONS 112 9.1.6 MAGNITUDE 112 9.1.7 THE ALGEBRA OF A EUCLIDEAN PLANE
113 9.1.8 THE ALGEBRA OF EUCLIDEAN 3-SPACE 114 9.1.9 THE ALGEBRA OF
SPACE-TIME 116 9.2 THE DIRAC EQUATION WITHOUT COMPLEX NUMBERS 116 9.3
OBSERVABLES AND THE WAVE FUNCTION 118 9.4 GENERATORS OF ROTATIONS IN
SPACE-TIME: INTRINSIC SPIN 120 9.4.1 GENERAL OBSERVATIONS 121 9.5 FIBER
BUNDLES AND QUANTUM THEORY VIS-A-VIS THE GEOMETRIC ALGEBRA APPROACH 122
9.6 FIBER BUNDLE PICTURE OF THE NEUTRON INTERFEROMETER EXPERIMENT 122
9.6.1 MULTIVECTOR ALGEBRA 125 9.6.2 LORENTZ ROTATIONS 127 9.6.3
CONCLUSION 129 9.7 CHARGE CONJUGATION 132 APPENDIX A 133 REFERENCES 134
10 QUANTUM GRAVITY IN REAL SPACE-TIME (COMMUTATORS AND ANTICOMMUTATORS)
137 10.1 QUANTUM GRAVITY AND GEOMETRIC ALGEBRA 137 10.2 QUANTUM GRAVITY
AND TORSION 140 10.3 QUANTUM GRAVITY IN REAL SPACE-TIME 142 10.4 A
QUADRATIC HAMILTONIAN 146 10.5 SPIN FLUCTUATIONS 149 10.6 SOME REMARKS
AND CONCLUSIONS 154 APPENDIX A: COMMUTATOR AND ANTICOMMUTATOR 156
REFERENCES 158 INDEX 159
|
| adam_txt |
GEOMETRIC ALGEBRA AND APPLICATIONS TO PHYSICS VENZO DE SABBATA BIDYUT
KUMAR DATTA TAYLOR &. FRANCIS TAYLOR & FRANCIS CROUP NEW YORK LONDON
TAYLOR & FRANCIS IS AN IMPRINT OF THE TAYLOR & FRANCIS CROUP, AN INFORMA
BUSINESS CONTENTS PART 1 1 1 THE BASIS FOR GEOMETRIC ALGEBRA 3 1.1
INTRODUCTION 3 1.2 GENESIS OF GEOMETRIC ALGEBRA 4 1.3 MATHEMATICAL
ELEMENTS OF GEOMETRIC ALGEBRA 10 1.4 GEOMETRIC ALGEBRA AS A SYMBOLIC
SYSTEM 13 1.5 GEOMETRIC ALGEBRA AS AN AXIOMATIC SYSTEM (AXIOM A) 18 1.6
SOME ESSENTIAL FORMULAS AND DEFINITIONS 23 REFERENCES 26 2 MULTIVECTORS
27 2.1 GEOMETRIC PRODUCT OF TWO BIVECTORS A AND B 27 2.2 OPERATION OF
REVERSION 29 2.3 MAGNITUDE OF A MULTIVECTOR 30 2.4 DIRECTIONS AND
PROJECTIONS 30 2.5 ANGLES AND EXPONENTIAL FUNCTIONS (AS OPERATORS) 34
2.6 EXPONENTIAL FUNCTIONS OF MULTIVECTORS 37 REFERENCES 39 3 EUCLIDEAN
PLANE 41 3.1 THE ALGEBRA OF EUCLIDEAN PLANE 41 3.2 GEOMETRIC
INTERPRETATION OF A BIVECTOR OF EUCLIDEAN PLANE 44 3.3 SPINOR /-PLANE 45
3.3.1 CORRESPONDENCE BETWEEN THE /-PLANE OF VECTORS AND THE SPINOR PLANE
47 3.4 DISTINCTION BETWEEN VECTOR AND SPINOR PLANES 47 3.4.1 SOME
OBSERVATIONS 49 3.5 THE GEOMETRIC ALGEBRA OF A PLANE 50 REFERENCES 51 4
THE PSEUDOSCALAR AND IMAGINARY UNIT 53 4.1 THE GEOMETRIC ALGEBRA OF
EUCLIDEAN 3-SPACE 53 4.1.1 THE PSEUDOSCALAR OF E 3 56 4.2 COMPLEX
CONJUGATION 57 APPENDIX A: SOME IMPORTANT RESULTS 57 REFERENCES 58 5
REAL DIRAC ALGEBRA :. 59 5.1 GEOMETRIC SIGNIFICANCE OF THE DIRAC
MATRICES Y M 59 5.2 GEOMETRIC ALGEBRA OF SPACE-TIME 60 5.3 CONJUGATIONS
64 5.3.1 CONJUGATE MULTIVECTORS (REVERSION) 64 5.3.2 SPACE-TIME
CONJUGATION 65 5.3.3 SPACE CONJUGATION 65 5.3.4 HERMITIAN CONJUGATION 65
5.4 LORENTZ ROTATIONS 66 5.5 SPINOR THEORY OF ROTATIONS IN
THREE-DIMENSIONAL EUCLIDEAN SPACE 69 REFERENCES 72 6 SPINOR AND
QUATERNION ALGEBRA 75 6.1 SPINOR ALGEBRA: QUATERNION ALGEBRA 75 6.2
VECTOR ALGEBRA 77 6.3 CLIFFORD ALGEBRA: GRAND SYNTHESIS OF ALGEBRA OF
GRASSMANN AND HAMILTON AND THE GEOMETRIC ALGEBRA OF HESTENES 78
REFERENCES 80 PART II 81 7 MAXWELL EQUATIONS 83 7.1 MAXWELL EQUATIONS IN
MINKOWSM SPACE-TIME 83 7.2 MAXWELL EQUATIONS IN RIEMANN SPACE-TIME (V4
MANIFOLD) 85 7.3 MAXWELL EQUATIONS IN RIEMANN-CARTAN SPACE-TIME (U4
MANIFOLD) 86 7.4 MAXWELL EQUATIONS IN TERMS OF SPACE-TIME ALGEBRA (STA)
88 REFERENCES 91 8 ELECTROMAGNETIC FIELD IN SPACE AND TIME (POLARIZATION
OF ELECTROMAGNETIC WAVES) 93 8.1 ELECTROMAGNETIC (E.M.) WAVES AND
GEOMETRIC ALGEBRA 93 8.2 POLARIZATION OF ELECTROMAGNETIC WAVES 94 8.3
QUATERNION FORM OF MAXWELL EQUATIONS FROM THE SPINOR FORM OF STA 97 8.4
MAXWELL EQUATIONS IN VECTOR ALGEBRA FROM THE QUATERNION (SPINOR)
FORMALISM 99 8.5 MAJORANA-WEYL EQUATIONS FROM THE QUATERNION (SPINOR)
FORMALISM OF MAXWELL EQUATIONS 100 APPENDIX A: COMPLEX NUMBERS IN
ELECTRODYNAMICS 103 APPENDIX B: PLANE-WAVE SOLUTIONS TO MAXWELL
EQUATIONS * POLARIZATION OF E.M. WAVES 105 REFERENCES 107 9 GENERAL
OBSERVATIONS AND GENERATORS OF ROTATIONS (NEUTRON INTERFEROMETER
EXPERIMENT) 109 9.1 REVIEW OF SPACE-TIME ALGEBRA (STA) 109 9.1.1 NOTE
110 9.1.2 MULTIVECTORS ILL 9.1.3 REVERSION ILL 9.1.4 LORENTZ ROTATION K
ILL 9.1.5 TWO SPECIAL CLASSES OF LORENTZ ROTATIONS: BOOSTS AND SPATIAL
ROTATIONS 112 9.1.6 MAGNITUDE 112 9.1.7 THE ALGEBRA OF A EUCLIDEAN PLANE
113 9.1.8 THE ALGEBRA OF EUCLIDEAN 3-SPACE 114 9.1.9 THE ALGEBRA OF
SPACE-TIME 116 9.2 THE DIRAC EQUATION WITHOUT COMPLEX NUMBERS 116 9.3
OBSERVABLES AND THE WAVE FUNCTION 118 9.4 GENERATORS OF ROTATIONS IN
SPACE-TIME: INTRINSIC SPIN 120 9.4.1 GENERAL OBSERVATIONS 121 9.5 FIBER
BUNDLES AND QUANTUM THEORY VIS-A-VIS THE GEOMETRIC ALGEBRA APPROACH 122
9.6 FIBER BUNDLE PICTURE OF THE NEUTRON INTERFEROMETER EXPERIMENT 122
9.6.1 MULTIVECTOR ALGEBRA 125 9.6.2 LORENTZ ROTATIONS 127 9.6.3
CONCLUSION 129 9.7 CHARGE CONJUGATION 132 APPENDIX A 133 REFERENCES 134
10 QUANTUM GRAVITY IN REAL SPACE-TIME (COMMUTATORS AND ANTICOMMUTATORS)
137 10.1 QUANTUM GRAVITY AND GEOMETRIC ALGEBRA 137 10.2 QUANTUM GRAVITY
AND TORSION 140 10.3 QUANTUM GRAVITY IN REAL SPACE-TIME 142 10.4 A
QUADRATIC HAMILTONIAN 146 10.5 SPIN FLUCTUATIONS 149 10.6 SOME REMARKS
AND CONCLUSIONS 154 APPENDIX A: COMMUTATOR AND ANTICOMMUTATOR 156
REFERENCES 158 INDEX 159 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T16:02:27Z |
| indexdate | 2024-07-09T20:46:00Z |
| institution | BVB |
| isbn | 1584887729 9781584887720 |
| language | English |
| lccn | 2006050868 |
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| physical | 168 S. graph. Darst. |
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| publisher | Taylor & Francis |
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| spelling | Sabbata, Venzo de Verfasser aut Geometric algebra and applications to physics Venzo de Sabbata and Bidyut Kumar Datta New York [u.a.] Taylor & Francis 2007 168 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematische Physik Geometry, Algebraic Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Geometrische Algebra (DE-588)4156707-9 gnd rswk-swf Geometrische Algebra (DE-588)4156707-9 s DE-604 Mathematische Physik (DE-588)4037952-8 s Datta, Bidyut K. Sonstige oth http://www.loc.gov/catdir/enhancements/fy0702/2006050868-d.html Publisher description GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015058999&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sabbata, Venzo de Geometric algebra and applications to physics Mathematische Physik Geometry, Algebraic Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd Geometrische Algebra (DE-588)4156707-9 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4156707-9 |
| title | Geometric algebra and applications to physics |
| title_auth | Geometric algebra and applications to physics |
| title_exact_search | Geometric algebra and applications to physics |
| title_exact_search_txtP | Geometric algebra and applications to physics |
| title_full | Geometric algebra and applications to physics Venzo de Sabbata and Bidyut Kumar Datta |
| title_fullStr | Geometric algebra and applications to physics Venzo de Sabbata and Bidyut Kumar Datta |
| title_full_unstemmed | Geometric algebra and applications to physics Venzo de Sabbata and Bidyut Kumar Datta |
| title_short | Geometric algebra and applications to physics |
| title_sort | geometric algebra and applications to physics |
| topic | Mathematische Physik Geometry, Algebraic Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd Geometrische Algebra (DE-588)4156707-9 gnd |
| topic_facet | Mathematische Physik Geometry, Algebraic Mathematical physics Geometrische Algebra |
| url | http://www.loc.gov/catdir/enhancements/fy0702/2006050868-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015058999&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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