Noncommutative geometry and the standard model of elementary particle physics:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2002
|
| Schriftenreihe: | Lecture notes in physics
596 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 346 S. |
| ISBN: | 3540440712 |
Internformat
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| 245 | 1 | 0 | |a Noncommutative geometry and the standard model of elementary particle physics |c F. Scheck ... (ed.) |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
| 300 | |a XII, 346 S. | ||
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| 490 | 1 | |a Lecture notes in physics |v 596 | |
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| 650 | 7 | |a Física |2 larpcal | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Mathematical physics |v Congresses | |
| 650 | 4 | |a Noncommutative differential geometry |v Congresses | |
| 650 | 4 | |a Standard model (Nuclear physics) |x Mathematics |v Congresses | |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS PART I. FOUNDATIONS OF NONCOMMUTATIVE GEOMETRY AND BASIC MODEL
BUILDING RALF HOLTKAMP 1 SPECTRAL TRIPLES AND ABSTRACT YANG-MILLS
FUNCTIONAL . . . . . . . . . . . . . 4 1.1 SPECTRAL TRIPLES . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 UNIVERSAL DIFFERENTIAL GRADED ALGEBRA . . . . . . . . . . . . . . .
. . . . . . 5 1.3 VECTOR POTENTIALS, UNIVERSAL CONNECTIONS. . . . . . .
. . . . . . . . . . . . 5 1.4 QUOTIENT DIFFERENTIAL GRADED ALGEBRA. . .
. . . . . . . . . . . . . . . . . . . 6 1.5 INNER PRODUCT . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 CURVATURE AND YANG-MILLS FUNCTIONAL . . . . . . . . . . . . . . . .
. . . . . . 8 RALF MEYER 2 REAL SPECTRAL TRIPLES AND CHARGE CONJUGATION
. . . . . . . . . . . . . . . . . . 11 2.1 REAL STRUCTURES ON EVEN
SPECTRAL TRIPLES . . . . . . . . . . . . . . . . . . 11 2.2 SPINC C
MANIFOLDS AND CHARGE CONJUGATION . . . . . . . . . . . . . . . . . 13
2.3 REAL STRUCTURES VIA CLIFFORD ALGEBRAS . . . . . . . . . . . . . . .
. . . . . . . 15 2.4 REAL STRUCTURES OF ODD DIMENSION . . . . . . . . .
. . . . . . . . . . . . . . . 17 2.5 RELATIONS TO REAL K-HOMOLOGY . . .
. . . . . . . . . . . . . . . . . . . . . . . . 18 2.6 REAL STRUCTURES
ON THE NC TORUS . . . . . . . . . . . . . . . . . . . . . . . . . 20
MICHAEL FRANK 3 THE COMMUTATIVE CASE: SPINORS, DIRAC OPERATOR AND DE
RHAM ALGEBRA . . . . . . . . . . . . . . . . . . 21 3.1 THE THEOREMS BY
GEL*FAND AND SERRE-SWAN . . . . . . . . . . . . . . . . 21 3.2 HERMITEAN
STRUCTURES AND FRAMES FOR SETS OF SECTIONS . . . . . . . 26 3.3 CLIFFORD
AND SPINOR BUNDLES, SPIN MANIFOLDS . . . . . . . . . . . . . . . 28 3.4
SPIN CONNECTION AND DIRAC OPERATOR . . . . . . . . . . . . . . . . . . .
. . . 31 3.5 THE UNIVERSAL DIFFERENTIAL ALGEBRA *C * ( M ) AND CONNES*
DIFFERENTIAL ALGEBRA * D / C * ( M ) . . . . . . . . . . . . . . . 33
3.6 THE EXTERIOR ALGEBRA BUNDLE * ( M ) AND THE DE RHAM COMPLEX 35 3.7 *
D / C * ( M ) VERSUS * ( M ) . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 36 X CONTENTS PETER M. ALBERTI AND REINER MATTHES 4
CONNES* TRACE FORMULA AND DIRAC REALIZATION OF MAXWELL AND YANG-MILLS
ACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1
GENERALITIES ON TRACES ON C * - AND W * -ALGEBRAS . . . . . . . . . . .
. . 40 4.2 EXAMPLES OF TRACES . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 43 4.3 EXAMPLES OF SINGULAR TRACES ON B
( H ) . . . . . . . . . . . . . . . . . . . . . 49 4.4 CALCULATING THE
DIXMIER TRACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5 THE CONNES* TRACE THEOREM AND ITS APPLICATION, PRELIMINARIES . . . .
. . . . . . . . . . . . . . . . . . . . . 60 4.6 CONNES* TRACE THEOREM .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.7
CLASSICAL YANG-MILLS ACTIONS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 72 BERND AMMANN AND CHRISTIAN B¨ AR 5 THE EINSTEIN-HILBERT
ACTION AS A SPECTRAL ACTION . . . . . . . . . . . . . . . . 75 5.1
GENERALIZED LAPLACIANS AND THE HEAT EQUATION . . . . . . . . . . . . .
75 5.2 THE FORMAL HEAT KERNEL . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 80 5.3 DIRAC OPERATORS AND WEITZENB¨ OCK
FORMULAS . . . . . . . . . . . . . . . . 88 5.4 INTEGRATION AND DIXMIER
TRACE. . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.5
VARIATIONAL FORMULAS AND THE EINSTEIN-HILBERT ACTION . . . . . . . 93
5.6 EINSTEIN-HILBERT ACTION AND WODZICKI RESIDUE . . . . . . . . . . . .
. . 101 RYSZARD NEST, ELMAR VOGT, AND WEND WERNER 6 SPECTRAL ACTION AND
THE CONNES-CHAMSEDINNE MODEL . . . . . . . . . . . . 109 6.1 THE
SPECTRAL ACTION PRINCIPLE . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 109 6.2 EXAMPLE: GRAVITY COUPLED TO ONE GAUGE FIELD . . . . .
. . . . . . . . 111 6.3 ASYMPTOTIC EXPANSION . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 113 6.4 FIRST EXAMPLE, FINAL
CALCULATION . . . . . . . . . . . . . . . . . . . . . . . . . 117 6.5
GRAVITY COUPLED TO THE STANDARD MODEL . . . . . . . . . . . . . . . . .
. . 127 PART II. THE LAGRANGIAN OF THE STANDARD MODEL DERIVED FROM
NONCOMMUTATIVE GEOMETRY HERALD UPMEIER 7 DIRAC OPERATOR AND REAL
STRUCTURE ON EUCLIDEAN AND MINKOWSKI SPACETIME . . . . . . . . . . . . .
. . . . . . . . . . . 136 7.1 * -MATRICES ON FLAT AND CURVED SPACETIME .
. . . . . . . . . . . . . . . . 136 7.2 LEVI-CIVITA CONNECTION AND DIRAC
OPERATOR . . . . . . . . . . . . . . . . 144 7.3 REAL STRUCTURE ON
SPACETIME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.4 TRACE FORMULAS AND INNER PRODUCTS . . . . . . . . . . . . . . . . .
. . . . . . 150 KAREN ELSNER, HOLGER NEUMANN, AND HARALD UPMEIER 8 THE
ELECTRO-WEAK MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 152 8.1 NONCOMMUTATIVE MATTER FIELDS . . . . . . . .
. . . . . . . . . . . . . . . . . . . 152 8.2 NONCOMMUTATIVE GAUGE
FIELDS . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 8.3
NONCOMMUTATIVE GAUGE ACTION FUNCTIONAL . . . . . . . . . . . . . . . . .
165 8.4 NONCOMMUTATIVE MATTER ACTION FUNCTIONAL . . . . . . . . . . . .
. . . . 170 CONTENTS XI KAREN ELSNER, HOLGER NEUMANN, AND HARALD UPMEIER
9 THE FULL STANDARD MODEL . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 172 9.1 NONCOMMUTATIVE MATTER FIELDS . . . .
. . . . . . . . . . . . . . . . . . . . . . . 172 9.2 NONCOMMUTATIVE
GAUGE FIELDS . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
9.3 NONCOMMUTATIVE GAUGE ACTION FUNCTIONAL . . . . . . . . . . . . . . .
. . 206 9.4NONCOMMUTATIVE MATTER ACTION FUNCTIONAL . . . . . . . . . . .
. . . . . 211 HOLGER NEUMANN AND HARALD UPMEIER 10 STANDARD MODEL
COUPLED WITH GRAVITY . . . . . . . . . . . . . . . . . . . . . . . . .
216 10.1 GENERALIZED DIRAC OPERATORS . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 216 10.2 SPECTRAL ACTION AND HEAT KERNEL
INVARIANTS . . . . . . . . . . . . . . . . 224 FLORIAN SCHECK 11 THE
HIGGS MECHANISM AND SPONTANEOUS SYMMETRY BREAKING . . . . . . 230 11.1
HISTORICAL NOTE . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 230 11.2 SPONTANEOUS SYMMETRY BREAKING AND
GOLDSTONE THEOREM . . . 232 11.3 SPONTANEOUS SYMMETRY BREAKING IN
YANG-MILLS THEORY . . . . . . 234 11.4THE CASE OF THE ELECTROWEAK MODEL:
BOSONIC SECTOR . . . . . . . . . 235 11.5 ELECTROWEAK MODEL: ADDING
QUARKS AND LEPTONS . . . . . . . . . . . . 238 11.6 REMARKS ABOUT
FERMIONIC MASS GENERATION . . . . . . . . . . . . . . . . 24 0 PART III.
NEW DIRECTIONS IN NONCOMMUTATIVE GEOMETRY AND MATHEMATICAL PHYSICS BRUNO
IOCHUM 12 THE IMPACT OF NC GEOMETRY IN PARTICLE PHYSICS. . . . . . . . .
. . . . . . . . 24 4 12.1 WHY NONCOMMUTATIVE GEOMETRY? . . . . . . . . .
. . . . . . . . . . . . . . . 24 4 12.2 SPECTRAL TRIPLES . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5
12.3 TECHNICAL POINTS . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 24 7 12.4THE NONCOMMUTATIVE HIG HWAY . . .
. . . . . . . . . . . . . . . . . . . . . . . . 24 8 12.5 COMPUTATION OF
HIGGS AND W MASSES . . . . . . . . . . . . . . . . . . . . . . 252 12.6
PARAMETER COUNTING . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 253 12.7 THE RENORMALIZATION MACHINERY . . . . . . . .
. . . . . . . . . . . . . . . . . . 255 12.8 NONCOMMUTATIVE RELATIVITY .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 12.9
CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 258 RAINER H¨ AUSSLING 13 THE SU (2 | 1)
MODEL OF ELECTROWEAK INTERACTIONS AND ITS CONNECTION TO NC GEOMETRY . .
. . . . . . . . . . . . . . . . . . . . . . . . . 260 13.1 INTRODUCTION
AND MOTIVATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
260 13.2 THE BOSONIC PART OF THE MODEL . . . . . . . . . . . . . . . . .
. . . . . . . . . . 260 13.3 THE FERMIONIC PART OF THE MODEL . . . . . .
. . . . . . . . . . . . . . . . . . . 267 13.4THE CONNECTION TO THE
CONNES-LOTT MODEL . . . . . . . . . . . . . . . . . 269 13.5 CONCLUSIONS
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 270 XII CONTENTS KLAUS FREDENHAGEN 14QUANTUM FIELDS AND
NONCOMMUTATIVE SPACETIME . . . . . . . . . . . . . . . . 271 14.1
NONCOMMUTATIVE SPACETIME AND UNCERTAINTY RELATIONS . . . . . . 271 14.2
NONCOMMUTATIVE SPACETIME AND QUANTUM FIELD THEORY . . . . . 273 14.3
INTERACTIONS AND NONCOMMUTATIVE GEOMETRY . . . . . . . . . . . . . . .
274 14.4 GAUGE THEORIES ON NONCOMMUTATIVE SPACETIME . . . . . . . . . .
. . . 276 EDWIN LANGMANN 15 NC GEOMETRY AND QUANTUM FIELDS: SIMPLE
EXAMPLES . . . . . . . . . . . . 278 15.1 INTRODUCTION . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
15.2 PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 279 15.3 STORY I: CHERN-SIMONS TERMS
FROM EFFECTIVE ACTIONS . . . . . . . . 284 15.4STORY II: REGULARIZATION:
ELEMENTARY EXAMPLES . . . . . . . . . . . . . 286 15.5 STORY III:
REGULARIZED TRACES OF OPERATORS . . . . . . . . . . . . . . . . . 288
15.6 STORY IV: YANG-MILLS ACTIONS FROM DIRAC OPERATORS . . . . . . . . .
294 15.7 FINAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 297 GIOVANNY LANDI 16 DIRAC EIGENVALUES
AS DYNAMICAL VARIABLES . . . . . . . . . . . . . . . . . . . . . . 299
16.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 299 16.2 NONCOMMUTATIVE GEOMETRY AND
GRAVITY . . . . . . . . . . . . . . . . . . . 300 16.3 FROM THE METRIC
TO THE EIGENVALUES . . . . . . . . . . . . . . . . . . . . . . . 303
16.4ACTION AND FIELD EQUATIONS . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 307 16.5 POISSON BRACKETS FOR THE EIGENVALUES . . . .
. . . . . . . . . . . . . . . . . . 309 16.6 FINAL REMARKS . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
RAIMAR WULKENHAAR 17 HOPF ALGEBRAS IN RENORMALIZATION AND NC GEOMETRY .
. . . . . . . . . . . 313 17.1 INTRODUCTORY REMARKS . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 313 17.2 THE HOPF
ALGEBRA OF CONNES*MOSCOVICI . . . . . . . . . . . . . . . . . . . . 313
17.3 ROOTED TREES . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 317 17.4FEYNMAN GRAPHS AND ROOTED TREES
. . . . . . . . . . . . . . . . . . . . . . . 319 17.5 A TOY MODEL:
ITERATED INTEGRALS . . . . . . . . . . . . . . . . . . . . . . . . . .
321 FEDELE LIZZI 18 NC GEOMETRY OF STRINGS AND DUALITY SYMMETRY . . . .
. . . . . . . . . . . . . 325 18.1 STRING THEORY AND T-DUALITY . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 325 18.2 INTERACTING
STRINGS AND SPECTRAL TRIPLES . . . . . . . . . . . . . . . . . . . . 328
18.3 COMPACTIFICATION AND NONCOMMUTATIVE TORUS . . . . . . . . . . . . .
. 333 18.4NONCOMMUTATIVE CONFIGURATION SPACE AND SPECTRAL GEOMETRY . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 18.5
CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 337 REFERENCES
.................................................... 338
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| genre | (DE-588)1071861417 Konferenzschrift 1999 Hesselberg gnd-content |
| genre_facet | Konferenzschrift 1999 Hesselberg |
| id | DE-604.BV014728575 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:05:33Z |
| institution | BVB |
| isbn | 3540440712 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009981408 |
| oclc_num | 50606495 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-384 |
| owner_facet | DE-355 DE-BY-UBR DE-384 |
| physical | XII, 346 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in physics |
| series2 | Lecture notes in physics Physics and astronomy online library |
| spelling | Noncommutative geometry and the standard model of elementary particle physics F. Scheck ... (ed.) Berlin [u.a.] Springer 2002 XII, 346 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 596 Physics and astronomy online library Física larpcal Mathematik Mathematische Physik Mathematical physics Congresses Noncommutative differential geometry Congresses Standard model (Nuclear physics) Mathematics Congresses Nichtkommutative Geometrie (DE-588)4171742-9 gnd rswk-swf Standardmodell Elementarteilchenphysik (DE-588)4297710-1 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1999 Hesselberg gnd-content Standardmodell Elementarteilchenphysik (DE-588)4297710-1 s Nichtkommutative Geometrie (DE-588)4171742-9 s DE-604 Scheck, Florian 1936-2024 Sonstige (DE-588)121611493 oth Lecture notes in physics 596 (DE-604)BV000003166 596 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009981408&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Noncommutative geometry and the standard model of elementary particle physics Lecture notes in physics Física larpcal Mathematik Mathematische Physik Mathematical physics Congresses Noncommutative differential geometry Congresses Standard model (Nuclear physics) Mathematics Congresses Nichtkommutative Geometrie (DE-588)4171742-9 gnd Standardmodell Elementarteilchenphysik (DE-588)4297710-1 gnd |
| subject_GND | (DE-588)4171742-9 (DE-588)4297710-1 (DE-588)1071861417 |
| title | Noncommutative geometry and the standard model of elementary particle physics |
| title_auth | Noncommutative geometry and the standard model of elementary particle physics |
| title_exact_search | Noncommutative geometry and the standard model of elementary particle physics |
| title_full | Noncommutative geometry and the standard model of elementary particle physics F. Scheck ... (ed.) |
| title_fullStr | Noncommutative geometry and the standard model of elementary particle physics F. Scheck ... (ed.) |
| title_full_unstemmed | Noncommutative geometry and the standard model of elementary particle physics F. Scheck ... (ed.) |
| title_short | Noncommutative geometry and the standard model of elementary particle physics |
| title_sort | noncommutative geometry and the standard model of elementary particle physics |
| topic | Física larpcal Mathematik Mathematische Physik Mathematical physics Congresses Noncommutative differential geometry Congresses Standard model (Nuclear physics) Mathematics Congresses Nichtkommutative Geometrie (DE-588)4171742-9 gnd Standardmodell Elementarteilchenphysik (DE-588)4297710-1 gnd |
| topic_facet | Física Mathematik Mathematische Physik Mathematical physics Congresses Noncommutative differential geometry Congresses Standard model (Nuclear physics) Mathematics Congresses Nichtkommutative Geometrie Standardmodell Elementarteilchenphysik Konferenzschrift 1999 Hesselberg |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009981408&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003166 |
| work_keys_str_mv | AT scheckflorian noncommutativegeometryandthestandardmodelofelementaryparticlephysics |