Quantum mechanics in the geometry of space-time: elementary theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Heidelberg [u.a.]
Springer
2011
|
| Schriftenreihe: | Springer briefs in physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XII, 130 S. |
| ISBN: | 9783642191992 9783642191985 3642191983 |
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Datensatz im Suchindex
| _version_ | 1809403888389849088 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
1 INTRODUCTION 1
REFERENCES 3
PART I THE REAL GEOMETRICAL ALGEBRA OR SPACE-TIME ALGEBRA. COMPARISON
WITH THE LANGUAGE OF THE COMPLEX MATRICES AND SPINORS
2 THE CLIFFORD ALGEBRA ASSOCIATED WITH THE MINKOWSKI SPACE-TIME M 7
2.1 THE CLIFFORD ALGEBRA ASSOCIATED WITH AN EUCLIDEAN SPACE . . 7 2.2
THE CLIFFORD ALGEBRAS AND THE "IMAGINARY NUMBER"V / -I. . . 9 2.3 THE
FIELD OF THE HAMILTON QUATERNIONS AND THE RING OF THE BIQUATERNION AS C/
+ (3,0) ANDC/(3,0) ~ C/ + (L,3) 10
REFERENCES 11
3 COMPARISON BETWEEN THE REAL AND THE COMPLEX LANGUAGE 13 3.1 THE
SPACE-TIME ALGEBRA AND THE WAVE FUNCTION ASSOCIATED WITH A PARTICLE: THE
HESTENES SPINOR 13
3.2 THE TAKABAYASI-HESTENES MOVING FRAME 15
3.3 EQUIVALENCES BETWEEN THE HESTENES AND THE DIRAC SPINORS . . 15 3.4
COMPARISON BETWEEN THE DIRAC AND THE HESTENES SPINORS . . . 16
REFERENCES 16
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1009641549
DIGITALISIERT DURCH
IMAGE 2
VIII CONTENTS
PART II THE U(L) GAUGE IN COMPLEX AND REAL LANGUAGES.
GEOMETRICAL PROPERTIES AND RELATION WITH THE SPIN AND THE ENERGY OF A
PARTICLE OF SPIN 1/2
4 GEOMETRICAL PROPERTIES OF THE U(L) GAUGE 21
4.1 THE DEFINITION OF THE GAUGE AND THE INVARIANCE OF A CHANGE OF GAUGE
IN THE U(L) GAUGE 21
4.1.1 THE U(L) GAUGE IN COMPLEX LANGUAGE 21
4.1.2 THE U(L) GAUGE INVARIANCE IN COMPLEX LANGUAGE 21
4.1.3 A PARADOX OF THE U(L) GAUGE IN COMPLEX LANGUAGE 22
4.2 THE U(L) GAUGE IN REAL LANGUAGE 22
4.2.1 THE DEFINITION OF THE U(L) GAUGE IN REAL LANGUAGE 23
4.2.2 THE U(L) GAUGE INVARIANCE IN REAL LANGUAGE 23 REFERENCES 24
5 RELATION BETWEEN THE U(L) GAUGE, THE SPIN AND THE ENERGY OF A PARTICLE
OF SPIN 1/2 25
5.1 RELATION BETWEEN THE U(L) GAUGE AND THE BIVECTOR SPIN . . . 25 5.2
RELATION BETWEEN THE U(L) GAUGE AND THE MOMENTUM-ENERGY TENSOR
ASSOCIATED WITH THE PARTICLE 25 5.3 RELATION BETWEEN THE U(L) GAUGE AND
THE ENERGY
OF THE PARTICLE 26
REFERENCES 26
PART III GEOMETRICAL PROPERTIES OF THE DIRAC THEORY OF THE ELECTRON
6 THE DIRAC THEORY OF THE ELECTRON IN REAL LANGUAGE 29
6. 1 THE HESTENES REAL FORM OF THE DIRAC EQUATION 29
6.2 THE PROBABILITY CURRENT 30
6.3 CONSERVATION OF THE PROBABILITY CURRENT 30
6.4 THE PROPER (BIVECTOR SPIN) AND THE TOTAL ANGULAR-MOMENTA 31
6.5 THE TETRODE ENERGY-MOMENTUM TENSOR 31
6.6 RELATION BETWEEN THE ENERGY OF THE ELECTRON AND THE INFINITESIMAL
ROTATION OF THE "SPIN PLANE" 32
6.7 THE TETRODE THEOREM 33
6.8 THE LAGRANGIAN OF THE DIRAC ELECTRON 33
6.9 UNITS 33
REFERENCES 34
IMAGE 3
CONTENTS
THE INVARIANT FORM OF THE DIRAC EQUATION AND INVARIANT PROPERTIES OF THE
DIRAC THEORY 35
7.1 THE INVARIANT FORM OF THE DIRAC EQUATION 35
7.2 THE PASSAGE FROM THE EQUATION OF THE ELECTRON TO THE ONE OF THE
POSITRON 36
7.3 THE FREE DIRAC ELECTRON, THE FREQUENCY AND THE CLOCK OF L. DE
BROGLIE 37
7.4 THE DIRAC ELECTRON, THE EINSTEIN FORMULA OF THE PHOTOEFFECT AND THE
L. DE BROGLIE FREQUENCY 39
7.5 THE EQUATION OF THE LORENTZ FORCE DEDUCED FROM THE DIRAC THEORY OF
THE ELECTRON 40
7.6 ON THE PASSAGES OF THE DIRAC THEORY TO THE CLASSICAL THEORY OF THE
ELECTRON 41
REFERENCES 41
PART IV THE SU(2) GAUGE AND THE YANG-MILLS THEORY IN COMPLEX AND REAL
LANGUAGES
8 GEOMETRICAL PROPERTIES OF THE SU(2) GAUGE AND THE ASSOCIATED
MOMENTUM-ENERGY TENSOR 45
8.1 THE SU(2) GAUGE IN THE GENERAL YANG-MILLS FIELD THEORY IN COMPLEX
LANGUAGE 45
8.2 THE SU(2) GAUGE AND THE Y.M. THEORY IN STA 46
8.2.1 THE SU(2) GAUGE AND THE GAUGE INVARIANCE IN STA 46
8.2.2 A MOMENTUM-ENERGY TENSOR ASSOCIATED WITH THE Y.M. THEORY 48
8.2.3 THE STA FORM OF THE Y.M. THEORY LAGRANGIAN 49
8.3 CONCLUSIONS ABOUT THE SU(2) GAUGE AND THE Y.M. THEORY . . 49
REFERENCES 50
PART V THE SU(2) X U(L) GAUGE IN COMPLEX AND REAL LANGUAGES
9 GEOMETRICAL PROPERTIES OF THE SU(2) X U(L) GAUGE 53
9.1 LEFT AND RIGHT PARTS OF A WAVE FUNCTION 53
9.2 LEFT AND RIGHT DOUBLETS ASSOCIATED WITH TWO WAVE FUNCTIONS 54
9.3 THE PART 5(7(2) OF THE SU(2) X F/(L) GAUGE 56
9.4 THE PART 1/(1) OF THE SU(2) X (/(I) GAUGE 56
9.5 GEOMETRICAL INTERPRETATION OF THE SU(2) X U{\) GAUGE OF A LEFT OR
RIGHT DOUBLET 56
IMAGE 4
CONTENTS
9.6 THE LAGRANGIAN IN THE SU(2) X [/(I) GAUGE 57
REFERENCES 57
PART VI THE GLASHOW-SALAM-WEINBERG ELECTROWEAK THEORY
10 THE ELECTROWEAK THEORY IN STA: GLOBAL PRESENTATION 61 10.1 GENERAL
APPROACH 61
10.2. THE PARTICLES AND THEIR WAVE FUNCTIONS 62
10.2.1 THE RIGHT AND LEFT PARTS OF THE WAVE FUNCTIONS OF THE NEUTRINO
AND THE ELECTRON 62
10.2.2 A LEFT DOUBLET AND TWO SINGLETS 62
10.3 THE CURRENTS ASSOCIATED WITH THE WAVE FUNCTIONS 62 10.3.1 THE
CURRENT ASSOCIATED WITH THE RIGHT AND LEFT PARTS OF THE ELECTRON AND
NEUTRINO 63
10.3.2 THE CURRENTS ASSOCIATED WITH THE LEFT DOUBLET 63 10.3.3 THE
CHARGE CURRENTS 64
10.4 THE BOSONS AND THE PHYSICAL CONSTANTS 65
10.4.1 THE PHYSICAL CONSTANTS 65
10.4.2 THE BOSONS 65
10.5 THE LAGRANGIAN 65
REFERENCES 66
11 THE ELECTROWEAK THEORY IN STA: LOCAL PRESENTATION 67 11.1 THE TWO
EQUIVALENT DECOMPOSITIONS OF THE PART LJ OF THE LAGRANGIAN 67
11.2 THE DECOMPOSITION OF THE PART L W OF THE LAGRANGIAN INTO A CHARGED
AND A NEUTRAL CONTRIBUTION 68
11.2.1 THE CHARGED CONTRIBUTION 69
11.2.2 THE NEUTRAL CONTRIBUTION 69
11.3 THE GAUGES 70
11.3.1 THE PART U(L) OF THE SU(2) X U(L) GAUGE 70
11.3.2 THE PART SU(2) OF THE SU(2) X U(L) GAUGE 71
11.3.3 ZITTERBEWEGUNG AND ELECTROWEAK CURRENTS IN DIRAC THEORY 71
REFERENCES 72
PART VII ON A CHANGE OF SU(3) INTO THREE SU(2) X U(L)
12 ON A CHANGE OF SU(3) INTO THREE SU(2) X U(L) 75
12.1 THE LIE GROUP SU(3) 75
12.1.1 THE GELL-MANN MATRICES L 75
IMAGE 5
CONTENTS
12.1.2 THE COLUMN ON WHICH THE GELL-MANN MATRICES ACT 76
12.1.3 EIGHT VECTORS G A 76
12.1.4 A LAGRANGIAN 76
12.1.5 ON THE ALGEBRAIC NATURE OF THE T* 76
12.1.6 COMMENTS 77
12.2 A PASSAGE FROM SU(3) TO THREE SU(2) X U(L) 77
12.3 AN ALTERNATIVE TO THE USE OF SU(3) IN QUANTUM CHROMODYNAMICS
THEORY? 79
REFERENCES 79
PART VIII ADDENDUM
13 A REAL QUANTUM ELECTRODYNAMICS 83
13.1 GENERAL APPROACH 83
13.2 ELECTROMAGNETISM: THE ELECTROMAGNETIC POTENTIAL 84
13.2.1 PRINCIPLES ON THE POTENTIAL 84
13.2.2 THE POTENTIAL CREATED BY A POPULATION OF CHARGES . . 85 13.2.3
NOTION OF CHARGE CURRENT 86
13.2.4 THE LORENTZ FORMULA OF THE RETARDED POTENTIALS 87 13.2.5 ON THE
INVARIANCES IN THE FORMULA OF THE RETARDED POTENTIALS 88
13.3 ELECTRODYNAMICS: THE ELECTROMAGNETIC FIELD, THE LORENTZ FORCE 89
13.3.1 GENERAL DEFINITION 89
13.3.2 CASE OF TWO PUNCTUAL CHARGES: THE COULOMB LAW . . 89 13.3.3
ELECTRIC AND MAGNETIC FIELDS 90
13.3.4 ELECTRIC AND MAGNETIC FIELDS DEDUCED FROM THE LORENTZ POTENTIAL
91
13.3.5 THE POYNTING VECTOR 93
13.4 ELECTRODYNAMICS IN THE DIRAC THEORY OF THE ELECTRON 93
13.4.1 THE DIRAC PROBABILITY CURRENTS 94
13.4.2 CURRENT ASSOCIATED WITH A LEVEL E OF ENERGY 94
13.4.3 EMISSION OF AN ELECTROMAGNETIC FIELD 95
13.4.4 SPONTANEOUS EMISSION 95
13.4.5 INTERACTION WITH A PLANE WAVE 96
13.4.6 THE LAMB SHIFT 100
REFERENCES 100
IMAGE 6
XII CONTENTS
PART IX APPENDICES
14 REAL ALGEBRAS ASSOCIATED WITH AN EUCLIDEAN SPACE 105 14.1 THE
GRASSMANN (OR EXTERIOR) ALGEBRA OF 71" 105
14.2 THE INNER PRODUCTS OF AN EUCLIDEAN SPACE E = N W ~ Q 105
14.3 THE CLIFFORD ALGEBRA CI(E) ASSOCIATED WITH AN EUCLIDEAN SPACE E = N
P "~ P 106
14.4 A CONSTRUCTION OF THE CLIFFORD ALGEBRA 108
14.5 THE GROUP O(E) IN CI(E) 109
REFERENCES 110
15 RELATION BETWEEN THE DIRAC SPINOR AND THE HESTENES SPINOR . . . I LL
15.1 THE PAULI SPINOR AND MATRICES I LL
15.2 THE DIRAC SPINOR I LL
15.3 THE QUATERNION AS A REAL FORM OF THE PAULI SPINOR 113 15.4 THE
BIQUATERNION AS A REAL FORM OF THE DIRAC SPINOR 114 REFERENCES 114
16 THE MOVEMENT IN SPACE-TIME OF A LOCAL ORTHONORMAL FRAME 115
16.1 C.I THE GROUP SO + (E) AND THE INFINITESIMAL ROTATIONS IN CL(E) 115
16.2 STUDY ON PROPERTIES OF LOCAL MOVING FRAMES 116
16.3 INFINITESIMAL ROTATION OF A LOCAL FRAME 116
16.4 INFINITESIMAL ROTATION OF LOCAL SUB-FRAMES 117
16.5 EFFECT OF A LOCAL FINITE ROTATION OF A LOCAL SUB-FRAME 118
REFERENCES 119
17 INCOMPATIBILITIES IN THE USE OF THE ISOSPIN MATRICES 121 17.1 *F IS
AN "ORDINARY" DIRAC SPINOR 121
17.2 IS A COUPLE Q A , FC ) OF DIRAC SPINORS 121
17.3 IS A RIGHT OR A LEFT DOUBLET 122
17.4 QUESTIONS ABOUT THE NATURE OF THE WAVE FUNCTION 122
18 A PROOF OF THE TETRODE THEOREM 123
19 ABOUT THE QUANTUM FIELDS THEORY 125
19.1 ON THE CONSTRUCTION OF THE QFT 125
19.2 QUESTIONS 126
19.3 AN ARTIFICE IN THE LAMB SHIFT CALCULATION 127
REFERENCES 128
INDEX 129 |
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| language | English |
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| spelling | Boudet, Roger 1928- Verfasser (DE-588)136967221 aut Quantum mechanics in the geometry of space-time elementary theory Roger Boudet Heidelberg [u.a.] Springer 2011 XII, 130 S. txt rdacontent n rdamedia nc rdacarrier Springer briefs in physics Literaturangaben Raum-Zeit (DE-588)4302626-6 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Raum-Zeit (DE-588)4302626-6 s Quantenmechanik (DE-588)4047989-4 s DE-604 Erscheint auch als Online-Ausgabe Quantum Mechanics in the Geometry of Space-Time X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3654976&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024484232&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boudet, Roger 1928- Quantum mechanics in the geometry of space-time elementary theory Raum-Zeit (DE-588)4302626-6 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4302626-6 (DE-588)4047989-4 |
| title | Quantum mechanics in the geometry of space-time elementary theory |
| title_auth | Quantum mechanics in the geometry of space-time elementary theory |
| title_exact_search | Quantum mechanics in the geometry of space-time elementary theory |
| title_full | Quantum mechanics in the geometry of space-time elementary theory Roger Boudet |
| title_fullStr | Quantum mechanics in the geometry of space-time elementary theory Roger Boudet |
| title_full_unstemmed | Quantum mechanics in the geometry of space-time elementary theory Roger Boudet |
| title_short | Quantum mechanics in the geometry of space-time |
| title_sort | quantum mechanics in the geometry of space time elementary theory |
| title_sub | elementary theory |
| topic | Raum-Zeit (DE-588)4302626-6 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Raum-Zeit Quantenmechanik |
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