New paths towards quantum gravity:
Saved in:
| Other Authors: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Series: | Lecture notes in physics
807 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XIX, 359 S. graph. Darst. |
| ISBN: | 9783642118968 |
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| 245 | 1 | 0 | |a New paths towards quantum gravity |c Bernhelm Booß-Bavnbek ... (ed.) |
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Record in the Search Index
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REFERENCES 54 CONTENTS PART I THREE PHYSICS VISIONS 1 NOTES ON "QUANTUM
GRAVITY" AND NONCOMMUTATIVE GEOMETRY 3 J.M. GRACIA-BONDIA 1.1
INTRODUCTION 3 1.2 GRAVITY AND EXPERIMENT: EXPECT THE UNEXPECTED 6 1.2.1
NONCOMMUTATIVE GEOMETRY I 10 1.2.2 WHERETO DIFFEOMORPHISM INVARIANCE? 10
1.3 GRAVITY FROM GAUGE INVARIANCE IN FIELD THEORY 13 1.3.1 PRELIMINARY
REMARKS 14 1.3.2 EXEMPLI GRATIAE 15 1.3.3 THE FREE LAGRANGIAN 16 .3.4 A
CANONICAL SETTING 17 .3.5 WHAT TO EXPECT 19 .3.6 CAUSAL GAUGE INVARIANCE
BY BRUTE FORCE 21 .3.7 CGI AT ALL ORDERS: GOING FOR IT 25 .3.8 DETAILS
ON QUANTIZATION AND GRAVITON HELICITIES 27 .3.9 FINAL REMARKS 30 1.3.10
OTHER WAYS 31 1.4 THE UNIMODULAR THEORIES 31 1.5 THE NONCOMMUTATIVE
CONNECTION 34 1.5.1 PROLEGOMENA 34 1.5.2 IRONIES OF HISTORY 35 1.5.3
SPECTRAL TRIPLES 36 .5.4 ON THE RECONSTRUCTION THEOREM 40 .5.5 THE
NONCOMMUTATIVE TORUS 41 .5.6 THE NONCOMPACT CASE 43 .5.7 NC TORIC
MANIFOLDS (COMPACT AND NONCOMPACT) 45 .5.8 CLOSING POINTS 46 1.5.9 SOME
INTERFACES WITH QUANTUM GRAVITY 51 1.6 MORE ON THE "COSMOLOGICAL
CONSTANT PROBLEM" AND THE ASTROPARTICLE INTERFACE 51 BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/1002586798 DIGITALISIERT DURCH I CONTENTS
QUANTUM GRAVITY AS SUM OVER SPACETIMES 59 J. AMBJ0RN, J. JURKIEWICZ AND
R. LOLL 2.1 INTRODUCTION 59 2.2 CDT 66 2.3 NUMERICAL RESULTS 74 2.3.1
THE EMERGENT DE SITTER BACKGROUND 75 2.3.2 FLUCTUATIONS AROUND DE SITTER
SPACE 79 2.3.3 THE SIZE OF THE UNIVERSE AND THE FLOW OF G 83 2.4
TWO-DIMENSIONAL EUCLIDEAN QUANTUM GRAVITY 87 2.4.1 CONTINUUM FORMULATION
87 2.4.2 THE LATTICE REGULARIZATION 89 2.4.3 COUNTING GRAPHS 93 2.4.4
THE CONTINUUM LIMIT 98 2.5 TWO-DIMENSIONAL LORENTZIAN QUANTUM GRAVITY
102 2.6 MATRIX MODEL REPRESENTATION 109 2.6.1 THE LOOP EQUATIONS 112
2.6.2 SUMMATION OVER ALL GENERA IN THE CDT MATRIX MODEL 116 2.7
DISCUSSION AND PERSPECTIVES 119 REFERENCES 1 22 LECTURES ON QUANTIZATION
OF GAUGE SYSTEMS 125 N. RESHETIKHIN 3.1 INTRODUCTION 125 3.2 LOCAL
LAGRANGIAN CLASSICAL FIELD THEORY 127 3.2.1 SPACE - TIME CATEGORIES 127
3.2.2 LOCAL LAGRANGIAN CLASSICAL FIELD THEORY '28 3.2.3 CLASSICAL
MECHANICS 128 3.2.4 FIRST-ORDER CLASSICAL MECHANICS 129 3.2.5 SCALAR
FIELDS 130 3.2.6 PURE EUCLIDEAN D -DIMENSIONAL YANG-MILLS 131 3.2.7
YANG-MILLS FIELD THEORY WITH MATTER 131 3.2.8 THREE-DIMENSIONAL
CHERN-SIMONS THEORY 132 3.3 HAMILTONIAN LOCAL CLASSICAL FIELD THEORY 133
3.3. CONTENTS 3.6 FINITE-DIMENSIONAL FADDEEV-POPOV QUANTIZATION AND THE
BRST DIFFERENTIAL 153 3.6.1 FADDEEV-POPOV TRICK 153 3.6.2 FEYNMAN
DIAGRAMS WITH GHOST FERMIONS 156 3.6.3 GAUGE INDEPENDENCE 158 3.6.4
FEYNMAN DIAGRAMS FOR LINEAR CONSTRAINTS 159 3.6.5 THE BRST DIFFERENTIA]
161 3.7 SEMICLASSICAL QUANTIZATION OF A SCALAR BOSE FIELD 163 3.7.1
FORMAL SEMICLASSICAL QUANTUM MECHANICS 163 3.7.2 D 1 AND ULTRAVIOLET
DIVERGENCIES 167 3.8 THE YANG-MILLS THEORY 169 3.8.1 THE GAUGE FIXING
170 3.8.2 THE FADDEEV-POPOV ACTION AND FEYNMAN DIAGRAMS 170 3.8.3 THE
RENORMALIZATION 171 3.9 THE CHERN-SIMONS THEORY 173 3.9.1 THE GAUGE
FIXING 174 3.9.2 THE FADDEEV-POPOV ACTION IN THE CHERN-SIMONS THEORY.
174 3.9.3 VACUUM FEYNMAN DIAGRAMS AND INVARIANTS OF 3-MANIFOLDS .177
3.9.4 WILSON LOOPS AND INVARIANTS OF KNOTS 182 3.9.5 COMPARISON WITH
COMBINATORIAL INVARIANTS 186 REFERENCES 188 PART II NOVEL MATHEMATICAL
TOOLS 4 MATHEMATICAL TOOLS FOR CALCULATION OF THE EFFECTIVE ACTION IN
QUANTUM GRAVITY 1 93 I.G. AVRAMIDI 4.1 INTRODUCTION 193 4.2 EFFECTIVE
ACTION IN QUANTUM FIELD THEORY AND QUANTUM GRAVITY 195 4.2.1 NON-GAUGE
FIELD THEORIES 197 4.2.2 GAUGE FIELD THEORIES 203 4.2.3 QUANTUM GENERAL
RELATIVITY 205 4.3 HEAT KERNEL METHOD 208 4.3.1 LAPLACE-TYPE OPERATORS
209 4.3. II CONTENTS 4.5.5 GENERAL STRUCTURE OF HEAT KERNEL COEFFICIENTS
234 4.6 HIGH-ENERGY APPROXIMATION 236 4.7 LOW-ENERGY APPROXIMATION 238
4.7.1 ALGEBRAIC APPROACH 239 4.7.2 COVARIANTLY CONSTANT BACKGROUND IN
FLAT SPACE 241 4.7.3 HOMOGENEOUS BUNDLES OVER SYMMETRIC SPACES 245 4.8
LOW-ENERGY EFFECTIVE ACTION IN QUANTUM GENERAL RELATIVITY 255 REFERENCES
258 LECTURES ON COHOMOLOGY, T-DUALITY, AND GENERALIZED GEOMETRY 261 P.
BOUWKNEGT 5.1 COHOMOLOGY AND DIFFERENTIAL CHARACTERS 261 5.1.1 A BRIEF
REVIEW OF DE RHAM AND CECH COHOMOLOGY 262 5.1.2 ELECTROMAGNETISM 264
5.1.3 THE CECH - DE RHAM COMPLEX 267 5.1.4 DIFFERENTIAL COHOMOLOGIES 270
5.2 T-DUALITY 276 5.2.1 INTRODUCTION TO T-DUALITY 276 5.2.2 THE BUSCHER
RULES 277 5.2.3 GYSIN SEQUENCES AND DIMENSIONAL REDUCTION 282 5.2.4
T-DUALITY = TAKAI DUALITY 285 5.2.5 T-DUALITY AS A DUALITY OF LOOP GROUP
BUNDLES 287 5.3 GENERALIZED GEOMETRY 290 5.3.1 CARTAN RELATIONS 291
5.3.2 LIE ALGEBROIDS 292 5.3.3 GENERALIZED GEOMETRY 293 5.3.4 COURANT
ALGEBROIDS 297 5.3.5 GENERALIZED COMPLEX GEOMETRY 303 5.3.6 T-DUALITY IN
GENERALIZED GEOMETRY 307 REFERENCES 309 STOCHASTIC GEOMETRY AND QUANTUM
GRAVITY: SOME RIGOROUS RESULTS .313 H. ZESSIN 6.1 AN AXIOMATIC
INTRODUCTION INTO REGGE'S MODEL 314 6.2 THE ZERO-INFINITY LAW OF
STOCHASTIC GEOMETRY AND THE CLUSTER PROCESS316 6.2. CONTENTS 6.3.2
POISSON-DELAUNAY SURFACES 326 6.3.3 SCHOLION: THE VORONOI CLUSTER
PROPERTY 327 6.4 ERGODIC BEHAVIOUR OF PX -SURFACES 328 6.4.1 PALM
MEASURES AND PALM DISTRIBUTIONS 328 6.4.2 AN ERGODIC THEOREM FOR
INTRINSIC METRIC QUANTITIES OF STATIONARY RANDOM SURFACES 329 6.4.3
CURVATURE PROPERTIES OF THE POISSON-DELAUNAY SURFACE 331 6.5 THE
TWO-DIMENSIONAL REGGE MODEL OF PURE QUANTUM GRAVITY 333 6.6 COMMENTS AND
FINAL DREAMS 334 REFERENCES 335 PART III AFTERTHOUGHTS 7 STEPS TOWARDS
QUANTUM GRAVITY AND THE PRACTICE OF SCIENCE: WILL THE MERGER OF
MATHEMATICS AND PHYSICS WORK? 339 B. BOOSS-BAVNBEK 7.1 REGARDING THE NEED
AND THE CHANCES OF UNIFICATION 339 7.2 THE PLACE OF PHYSICS IN JOHN
DEE'S GROUNDPLAT OF SCIENCES AND ARTES, MATHEMATICAL OF 1570 340 7.3
DELIMITATION BETWEEN MATHEMATICS AND PHYSICS 341 7.4 VARIETY OF
MODELLING PURPOSES 342 7.4.1 PRODUCTION OF DATA, MODEL-BASED
MEASUREMENTS 342 7.4.2 SIMULATION 343 7.4.3 PREDICTION 343 7.4.4 CONTROL
344 7.4.5 EXPLAIN PHENOMENA 345 7.4.6 THEORY DEVELOPMENT 346 7.5 "THE
TROUBLE WITH PHYSICS" 347 7.6 THEORY-MODEL-EXPERIMENT 347 7.6.1 FIRST
PRINCIPLES 348 7.6.2 TOWARDS A TAXONOMY OF MODELS 348 7.6.3 THE
SCIENTIFIC STATUS OF QUANTUM GRAVITY AS COMPARED TO MEDICINE AND
ECONOMICS 350 7.7 GENERAL TRENDS OF MATHEMATIZATION AND MODELLING 351
7.7. |
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| spelling | New paths towards quantum gravity Bernhelm Booß-Bavnbek ... (ed.) Berlin [u.a.] Springer 2010 XIX, 359 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 807 Literaturangaben Quantengravitation (DE-588)4124012-1 gnd rswk-swf Quantengravitation (DE-588)4124012-1 s DE-604 Booss-Bavnbek, Bernhelm 1941- (DE-588)108280470 edt Erscheint auch als Online-Ausgabe 978-3-642-11897-5 Lecture notes in physics 807 (DE-604)BV000003166 807 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3478440&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=020502360&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | New paths towards quantum gravity Lecture notes in physics Quantengravitation (DE-588)4124012-1 gnd |
| subject_GND | (DE-588)4124012-1 |
| title | New paths towards quantum gravity |
| title_auth | New paths towards quantum gravity |
| title_exact_search | New paths towards quantum gravity |
| title_full | New paths towards quantum gravity Bernhelm Booß-Bavnbek ... (ed.) |
| title_fullStr | New paths towards quantum gravity Bernhelm Booß-Bavnbek ... (ed.) |
| title_full_unstemmed | New paths towards quantum gravity Bernhelm Booß-Bavnbek ... (ed.) |
| title_short | New paths towards quantum gravity |
| title_sort | new paths towards quantum gravity |
| topic | Quantengravitation (DE-588)4124012-1 gnd |
| topic_facet | Quantengravitation |
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