Division algebras: octonions, quaternions, complex numbers and the algebraic design of physics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer
1994
|
| Schriftenreihe: | Mathematics and its applications
290 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 236 S. |
| ISBN: | 0792328906 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV009743636 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 940802s1994 |||| 00||| eng d | ||
| 020 | |a 0792328906 |9 0-7923-2890-6 | ||
| 035 | |a (OCoLC)832230430 | ||
| 035 | |a (DE-599)BVBBV009743636 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-703 |a DE-29T |a DE-20 |a DE-11 |a DE-19 | ||
| 082 | 0 | |a 512.57 | |
| 084 | |a SK 230 |0 (DE-625)143225: |2 rvk | ||
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 100 | 1 | |a Dixon, Geoffrey M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Division algebras |b octonions, quaternions, complex numbers and the algebraic design of physics |c by Geoffrey M. Dixon |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer |c 1994 | |
| 300 | |a X, 236 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 290 | |
| 650 | 0 | 7 | |a Mathematische Physik |0 (DE-588)4037952-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Divisionsalgebra |0 (DE-588)4138776-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Divisionsalgebra |0 (DE-588)4138776-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Divisionsalgebra |0 (DE-588)4138776-4 |D s |
| 689 | 1 | 1 | |a Mathematische Physik |0 (DE-588)4037952-8 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Mathematics and its applications |v 290 |w (DE-604)BV008163334 |9 290 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006444093&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006444093 | ||
Datensatz im Suchindex
| _version_ | 1804124088936955904 |
|---|---|
| adam_text | Table of Contents
I Underpinnings 1
1.1 The Argument 1
Screed I 1
Screed II 3
Screed III 7
1.2 Clifford Algebras 11
Clifford Algebra R3ii 16
Pauli Algebra 18
Clifford Algebra Ri,3 19
Clifford Algebra Ri,9 20
1.3 Conjugations and Spinors 22
Nilpotent Clifford Algebras 24
Symplectic Nilpotent Clifford Algebras 25
1.4 Algebraic Fundamentals of the Standard Model 29
II Division Algebras Alone 31
2.1 Mostly Octonions 31
2.2 Adjoint Algebras 35
2.3 Clifford Algebras, Spinors 40
2.4 Resolving the Identity of OL 43
2.5 Lie Algebras, Lie Groups, from Ol 46
2.6 From Galois Fields to Division Algebras: An Insight 49
III Tensor Algebras 59
3.1 Tensoring Two: Clifford Algebras and Spinors 59
3.2 Tensoring Two: Spinor Inner Product 61
Link to Internal Symmetry 64
3.3 Tensoring Three: Clifford Algebras and Spinors 66
3.4 Tensoring Three: Spinor Inner Product 68
Resolving the Identity of T 68
The Trace of X 70
3.5 Derivation of the Standard Symmetry 73
3.6 SU{2) x SU{2) Multiplets, and 17(1) 78
U{1) Charges 81
IV Connecting to Physics 83
4.1 Connecting to Geometry 83
Dimensional Reduction 85
4.2 Connecting to Particles 90
4.3 Parity Nonconservation 94
Righthanded Dirac Operator 94
Lefthanded Dirac Operator 95
Full Parity Violating Dirac Operator 96
4.4 Gauge Fields 97
4.5 Weak Mixing 100
4.6 Gauging SU(3) 105
V Spontaneous Symmetry Breaking 109
5.1 Scalar Fields 109
5.2 Scalar Lagrangians HI
5.3 Fermions and Scalars 115
VI 10 Dimensions 117
6.1 Fermion Lagrangian 117
Matter/Antimatter Mixing 120
6.2 More SU{3) 122
6.3 Freedom from Matter Antimatter Mixing 124
6.4 (1,9) Scalar Lagrangian 126
6.5 Charge Conjugation on TL(2) 128
6.6 Charge Conjugation on T2 130
The Meaning of Majorana 132
6.7 10 Other Dimensions 133
The Clifford Algebra 137
VII Doorways 141
7.1 Moufang and Other Identities 141
Two Identities 145
The Moufang Identities 148
7.2 Spheres and Lie Algebras 150
S3 151
S7 153
Sphere Fibrations 159
7.3 Triality 160
Triality Representations of so(8) 164
The Tri in Triality 165
Freudenthal s Principle of Triality 169
7.4 LG2 and Tri 170
LG2 Triality Triplet 171
7.5 LG2 Triplets and the X Product 175
LG$ General Solution 180
LG$ and the X Adjoint Algebra OLX 187
VIII Corridors 191
8.1 Magic Square 191
8.2 The Ten MSKK 192
8.3 SpinorxK1 Outer Products 198
C Outer Product 198
Q Outer Products 200
O Outer Products 202
8.4 LFi ~ MSRO 203
8.5 J3° and F4 208
8.6 More Magic Square 213
Appendix i. Oj, Actions: Product Rule eaea+ = ea+5 217
Appendix ii. Oh Actions: Product Rule eaea+ = ea+5 221
Appendix iii. Ol Actions: Product Rule eaea+i = ea+3 225
Appendix iv. Or Actions: Product Rule eaea+i = ea+3 229
Bibliography 233
Index 235
|
| any_adam_object | 1 |
| author | Dixon, Geoffrey M. |
| author_facet | Dixon, Geoffrey M. |
| author_role | aut |
| author_sort | Dixon, Geoffrey M. |
| author_variant | g m d gm gmd |
| building | Verbundindex |
| bvnumber | BV009743636 |
| classification_rvk | SK 230 SK 950 |
| ctrlnum | (OCoLC)832230430 (DE-599)BVBBV009743636 |
| dewey-full | 512.57 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.57 |
| dewey-search | 512.57 |
| dewey-sort | 3512.57 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01638nam a2200409 cb4500</leader><controlfield tag="001">BV009743636</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">940802s1994 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0792328906</subfield><subfield code="9">0-7923-2890-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)832230430</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV009743636</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-19</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.57</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 230</subfield><subfield code="0">(DE-625)143225:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dixon, Geoffrey M.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Division algebras</subfield><subfield code="b">octonions, quaternions, complex numbers and the algebraic design of physics</subfield><subfield code="c">by Geoffrey M. Dixon</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht u.a.</subfield><subfield code="b">Kluwer</subfield><subfield code="c">1994</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 236 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Mathematics and its applications</subfield><subfield code="v">290</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematische Physik</subfield><subfield code="0">(DE-588)4037952-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Divisionsalgebra</subfield><subfield code="0">(DE-588)4138776-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Divisionsalgebra</subfield><subfield code="0">(DE-588)4138776-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Divisionsalgebra</subfield><subfield code="0">(DE-588)4138776-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Mathematische Physik</subfield><subfield code="0">(DE-588)4037952-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematics and its applications</subfield><subfield code="v">290</subfield><subfield code="w">(DE-604)BV008163334</subfield><subfield code="9">290</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006444093&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-006444093</subfield></datafield></record></collection> |
| id | DE-604.BV009743636 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:40:07Z |
| institution | BVB |
| isbn | 0792328906 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006444093 |
| oclc_num | 832230430 |
| open_access_boolean | |
| owner | DE-12 DE-703 DE-29T DE-20 DE-11 DE-19 DE-BY-UBM |
| owner_facet | DE-12 DE-703 DE-29T DE-20 DE-11 DE-19 DE-BY-UBM |
| physical | X, 236 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Dixon, Geoffrey M. Verfasser aut Division algebras octonions, quaternions, complex numbers and the algebraic design of physics by Geoffrey M. Dixon Dordrecht u.a. Kluwer 1994 X, 236 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 290 Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Divisionsalgebra (DE-588)4138776-4 gnd rswk-swf Divisionsalgebra (DE-588)4138776-4 s DE-604 Mathematische Physik (DE-588)4037952-8 s Mathematics and its applications 290 (DE-604)BV008163334 290 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006444093&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dixon, Geoffrey M. Division algebras octonions, quaternions, complex numbers and the algebraic design of physics Mathematics and its applications Mathematische Physik (DE-588)4037952-8 gnd Divisionsalgebra (DE-588)4138776-4 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4138776-4 |
| title | Division algebras octonions, quaternions, complex numbers and the algebraic design of physics |
| title_auth | Division algebras octonions, quaternions, complex numbers and the algebraic design of physics |
| title_exact_search | Division algebras octonions, quaternions, complex numbers and the algebraic design of physics |
| title_full | Division algebras octonions, quaternions, complex numbers and the algebraic design of physics by Geoffrey M. Dixon |
| title_fullStr | Division algebras octonions, quaternions, complex numbers and the algebraic design of physics by Geoffrey M. Dixon |
| title_full_unstemmed | Division algebras octonions, quaternions, complex numbers and the algebraic design of physics by Geoffrey M. Dixon |
| title_short | Division algebras |
| title_sort | division algebras octonions quaternions complex numbers and the algebraic design of physics |
| title_sub | octonions, quaternions, complex numbers and the algebraic design of physics |
| topic | Mathematische Physik (DE-588)4037952-8 gnd Divisionsalgebra (DE-588)4138776-4 gnd |
| topic_facet | Mathematische Physik Divisionsalgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006444093&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT dixongeoffreym divisionalgebrasoctonionsquaternionscomplexnumbersandthealgebraicdesignofphysics |