Quantum gravitation: the Feynman path integral approach
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Berlin [u.a.]
Springer
2009
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Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XVII, 342 S. graph. Darst. |
ISBN: | 9783540852926 9783540852933 |
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245 | 1 | 0 | |a Quantum gravitation |b the Feynman path integral approach |c Herbert W. Hamber |
264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
300 | |a XVII, 342 S. |b graph. Darst. | ||
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adam_text | HERBERT W. HAMBER QUANTUM GRAVITATION THE FEYNMAN PATH INTEGRAL APPROACH
4Y SPRINGER CONTENTS CONTINUUM FORMULATION 1 1.1 GENERAL ASPECTS 1 1.2
MASSLESS SPIN TWO FIELD 1 1.3 WAVE EQUATION 2 1.4 FEYNMAN RULES 11 1.5_.
ONE-LOOP DIVERGENCES 16 1.6 GRAVITY IN D DIMENSIONS 21 1.7 HIGHER
DERIVATIVE TERMS 24 1.8 SUPERSYMMETRY 33 1.9 SUPERGRAVITY 37 1.10 STRING
THEORY 40 1.11 SUPERSYMMETRIC STRINGS * 48 FEYNMAN PATH INTEGRAL
FORMULATION 55 2.1 THE PATH INTEGRAL . 55 2.2 SUM OVER PATHS 56 2.3
EULIDEAN ROTATION 58 2.4 GRAVITATIONAL FUNCTIONAL MEASURE 59 2.5
CONFORMAL INSTABILITY 64 GRAVITY IN 2 + E DIMENSIONS 67 3.1 DIMENSIONAL
EXPANSION 67 3.2 PERTURBATIVELY NON-RENORMALIZABLE THEORIES: THE SIGMA
MODEL.... 68 3.3 NON-LINEAR SIGMA MODEL IN THE LARGE-N LIMIT 79 3.4
SELF-COUPLED FERMION MODEL 83 3.5 THE GRAVITATIONAL CASE 84 3.6 PHASES
OF GRAVITY IN 2+E DIMENSIONS 92 3.7 RUNNING OF A(/X) IN GAUGE THEORIES
98 CONTENTS HAMILTONIAN AND WHEELER-DEWITT EQUATION 103 4.1 CLASSICAL
INITIAL VALUE PROBLEM 103 4.2 FIRST ORDER FORMULATION 104 4.3
ARNOWITT-DESER-MISNER (ADM) FORMALISM 107 4.4 ORTHOGONAL DECOMPOSITION
IN THE LINEARIZED THEORY 110 4.5 INTRINSIC AND EXTRINSIC CURVATURE,
HAMILTONIAN ILL 4.6 MATTER SOURCE TERMS 112 4.7 WHEELER-DEWITT EQUATION
114 4.8 SEMICLASSICAL EXPANSION OF THE WHEELER-DEWITT EQUATION 115 4.9
CONNECTION WITH THE FEYNMAN PATH INTEGRAL 117 4.10 MINISUPERSPACE 118
4.11 SOLUTION OF SIMPLE MINISUPERSPACE MODELS 122 4.12 QUANTUM
HAMILTONIAN FOR GAUGE THEORIES 127 4.13 LATTICE REGULARIZED HAMILTONIAN
FOR GAUGE THEORIES 129 4.14 LATTICE HAMILTONIAN FOR QUANTUM GRAVITY 135
SEMICLASSICAL GRAVITY 141 5.1 COSMOLOGICAL WAVEFUNCTIONS 141 5.2
SEMICLASSICAL EXPANSION 146 5.3 PAIR CREATION IN CONSTANT ELECTRIC
FIELDS 152 5.4 BLACK HOLE PARTICLE EMISSION 154 5.5 METHOD OF IN AND OUT
VACUA 158 5.6 COMPLEX PERIODIC TIME 163 5.7 BLACK HOLE EVAPORATION 166
5.8 QUANTUM GRAVITY CORRECTIONS 167 LATTICE REGULARIZED QUANTUM GRAVITY
169 6.1 THE LATTICE THEORY 169 6.2 GENERAL FORMULATION 170 6.3 VOLUMES
AND ANGLES 171 6.4 ROTATIONS, PARALLEL TRANSPORTS AND VORONOI LOOPS 173
6.5 INVARIANT LATTICE ACTION 179 6.6 LATTICE DIFFEOMORPHISM INVARIANCE
184 6.7 LATTICE BIANCHI IDENTITIES 186 6.8 GRAVITATIONAL WILSON LOOP 188
6.9 LATTICE REGULARIZED PATH INTEGRAL 190 6.10 AN ELEMENTARY EXAMPLE 195
6.11 LATTICE HIGHER DERIVATIVE TERMS 198 6.12 SCALAR MATTER FIELDS 203
6.13 INVARIANCE PROPERTIES OF THE SCALAR ACTION 209 6.14 LATTICE
FERMIONS, TETRADS AND SPIN ROTATIONS 211 6.15 GAUGE FIELDS 213 6.16
LATTICE GRAVITINO .- 214 6.17 ALTERNATE DISCRETE FORMULATIONS 216 6.18
LATTICE INVARIANCE VERSUS CONTINUUM INVARIANCE 220 CONTENTS XVII 7
ANALYTICAL LATTICE EXPANSION METHODS 225 7.1 MOTIVATION 225 7.2 LATTICE
WEAK FIELD EXPANSION AND TRANSVERSE-TRACELESS MODES .... 225 7.3 LATTICE
DIFFEOMORPHISM INVARIANCE 234 7.4 STRONG COUPLING EXPANSION 242 7.5
GRAVITATIONAL WILSON LOOP 248 7.6 DISCRETE GRAVITY IN THE L&VGE-D LIMIT
260 7.7 MEAN FIELD THEORY 269 8 NUMERICAL STUDIES 273 8.1
NONPERTURBATIVE GRAVITY 273 8.2 OBSERVABLES, PHASE STRUCTURE AND
CRITICAL EXPONENTS 274 8.3 INVARIANT LOCAL GRAVITATIONAL AVERAGES 276
8.4 INVARIANT CORRELATIONS AT FIXED GEODESIC DISTANCE 278 8.5 WILSON
LINES AND STATIC POTENTIAL 281 8.6 SCALING IN THE VICINITY OF THE
CRITICAL POINT 284 8.7 PHYSICAL AND UNPHYSICAL PHASES 285 8.8 NUMERICAL
DETERMINATION OF THE SCALING EXPONENTS 290 8.9 RENORMALIZATION GROUP AND
LATTICE CONTINUUM LIMIT 295 8.10 CURVATURE SCALES 300 8.11 GRAVITATIONAL
CONDENSATE 302 9 SCALE DEPENDENT GRAVITATIONAL COUPLINGS 305 9.1
RENORMALIZATION GROUP AND SCALE DEPENDENCE OF G 305 9.2 EFFECTIVE FIELD
EQUATIONS 305 9.3 POISSON S EQUATION AND VACUUM POLARIZATION CLOUD 308
9.4 STATIC ISOTROPIC SOLUTION -. 311 9.5 COSMOLOGICAL SOLUTIONS 314 9.6
QUANTUM GRAVITY AND MACH S PRINCIPLE 321 REFERENCES 325 INDEX 335
|
adam_txt |
HERBERT W. HAMBER QUANTUM GRAVITATION THE FEYNMAN PATH INTEGRAL APPROACH
4Y SPRINGER CONTENTS CONTINUUM FORMULATION 1 1.1 GENERAL ASPECTS 1 1.2
MASSLESS SPIN TWO FIELD 1 1.3 WAVE EQUATION 2 1.4 FEYNMAN RULES 11 1.5_.
ONE-LOOP DIVERGENCES 16 1.6 GRAVITY IN D DIMENSIONS 21 1.7 HIGHER
DERIVATIVE TERMS 24 1.8 SUPERSYMMETRY 33 1.9 SUPERGRAVITY 37 1.10 STRING
THEORY 40 1.11 SUPERSYMMETRIC STRINGS * 48 FEYNMAN PATH INTEGRAL
FORMULATION 55 2.1 THE PATH INTEGRAL '. 55 2.2 SUM OVER PATHS 56 2.3
EULIDEAN ROTATION 58 2.4 GRAVITATIONAL FUNCTIONAL MEASURE 59 2.5
CONFORMAL INSTABILITY 64 GRAVITY IN 2 + E DIMENSIONS 67 3.1 DIMENSIONAL
EXPANSION 67 3.2 PERTURBATIVELY NON-RENORMALIZABLE THEORIES: THE SIGMA
MODEL. 68 3.3 NON-LINEAR SIGMA MODEL IN THE LARGE-N LIMIT 79 3.4
SELF-COUPLED FERMION MODEL 83 3.5 THE GRAVITATIONAL CASE 84 3.6 PHASES
OF GRAVITY IN 2+E DIMENSIONS 92 3.7 RUNNING OF A(/X) IN GAUGE THEORIES
98 CONTENTS HAMILTONIAN AND WHEELER-DEWITT EQUATION 103 4.1 CLASSICAL
INITIAL VALUE PROBLEM 103 4.2 FIRST ORDER FORMULATION 104 4.3
ARNOWITT-DESER-MISNER (ADM) FORMALISM 107 4.4 ORTHOGONAL DECOMPOSITION
IN THE LINEARIZED THEORY 110 4.5 INTRINSIC AND EXTRINSIC CURVATURE,
HAMILTONIAN ILL 4.6 MATTER SOURCE TERMS 112 4.7 WHEELER-DEWITT EQUATION
114 4.8 SEMICLASSICAL EXPANSION OF THE WHEELER-DEWITT EQUATION 115 4.9
CONNECTION WITH THE FEYNMAN PATH INTEGRAL 117 4.10 MINISUPERSPACE 118
4.11 SOLUTION OF SIMPLE MINISUPERSPACE MODELS 122 4.12 QUANTUM
HAMILTONIAN FOR GAUGE THEORIES 127 4.13 LATTICE REGULARIZED HAMILTONIAN
FOR GAUGE THEORIES 129 4.14 LATTICE HAMILTONIAN FOR QUANTUM GRAVITY 135
SEMICLASSICAL GRAVITY 141 5.1 COSMOLOGICAL WAVEFUNCTIONS 141 5.2
SEMICLASSICAL EXPANSION 146 5.3 PAIR CREATION IN CONSTANT ELECTRIC
FIELDS 152 5.4 BLACK HOLE PARTICLE EMISSION 154 5.5 METHOD OF IN AND OUT
VACUA 158 5.6 COMPLEX PERIODIC TIME 163 5.7 BLACK HOLE EVAPORATION 166
5.8 QUANTUM GRAVITY CORRECTIONS 167 LATTICE REGULARIZED QUANTUM GRAVITY
169 6.1 THE LATTICE THEORY 169 6.2 GENERAL FORMULATION 170 6.3 VOLUMES
AND ANGLES 171 6.4 ROTATIONS, PARALLEL TRANSPORTS AND VORONOI LOOPS 173
6.5 INVARIANT LATTICE ACTION 179 6.6 LATTICE DIFFEOMORPHISM INVARIANCE
184 6.7 LATTICE BIANCHI IDENTITIES 186 6.8 GRAVITATIONAL WILSON LOOP 188
6.9 LATTICE REGULARIZED PATH INTEGRAL 190 6.10 AN ELEMENTARY EXAMPLE 195
6.11 LATTICE HIGHER DERIVATIVE TERMS 198 6.12 SCALAR MATTER FIELDS 203
6.13 INVARIANCE PROPERTIES OF THE SCALAR ACTION 209 6.14 LATTICE
FERMIONS, TETRADS AND SPIN ROTATIONS 211 6.15 GAUGE FIELDS 213 6.16
LATTICE GRAVITINO .- 214 6.17 ALTERNATE DISCRETE FORMULATIONS 216 6.18
LATTICE INVARIANCE VERSUS CONTINUUM INVARIANCE 220 CONTENTS XVII 7
ANALYTICAL LATTICE EXPANSION METHODS 225 7.1 MOTIVATION 225 7.2 LATTICE
WEAK FIELD EXPANSION AND TRANSVERSE-TRACELESS MODES . 225 7.3 LATTICE
DIFFEOMORPHISM INVARIANCE 234 7.4 STRONG COUPLING EXPANSION 242 7.5
GRAVITATIONAL WILSON LOOP 248 7.6 DISCRETE GRAVITY IN THE L&VGE-D LIMIT
260 7.7 MEAN FIELD THEORY 269 8 NUMERICAL STUDIES 273 8.1
NONPERTURBATIVE GRAVITY 273 8.2 OBSERVABLES, PHASE STRUCTURE AND
CRITICAL EXPONENTS 274 8.3 INVARIANT LOCAL GRAVITATIONAL AVERAGES 276
8.4 INVARIANT CORRELATIONS AT FIXED GEODESIC DISTANCE 278 8.5 WILSON
LINES AND STATIC POTENTIAL 281 8.6 SCALING IN THE VICINITY OF THE
CRITICAL POINT 284 8.7 PHYSICAL AND UNPHYSICAL PHASES 285 8.8 NUMERICAL
DETERMINATION OF THE SCALING EXPONENTS 290 8.9 RENORMALIZATION GROUP AND
LATTICE CONTINUUM LIMIT 295 8.10 CURVATURE SCALES 300 8.11 GRAVITATIONAL
CONDENSATE 302 9 SCALE DEPENDENT GRAVITATIONAL COUPLINGS 305 9.1
RENORMALIZATION GROUP AND SCALE DEPENDENCE OF G 305 9.2 EFFECTIVE FIELD
EQUATIONS 305 9.3 POISSON'S EQUATION AND VACUUM POLARIZATION CLOUD 308
9.4 STATIC ISOTROPIC SOLUTION -. 311 9.5 COSMOLOGICAL SOLUTIONS 314 9.6
QUANTUM GRAVITY AND MACH'S PRINCIPLE 321 REFERENCES 325 INDEX 335 |
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id | DE-604.BV035188363 |
illustrated | Illustrated |
index_date | 2024-07-02T23:00:47Z |
indexdate | 2024-07-09T21:27:02Z |
institution | BVB |
isbn | 9783540852926 9783540852933 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016995018 |
oclc_num | 248994165 |
open_access_boolean | |
owner | DE-29T DE-703 DE-20 DE-634 DE-11 |
owner_facet | DE-29T DE-703 DE-20 DE-634 DE-11 |
physical | XVII, 342 S. graph. Darst. |
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spelling | Hamber, Herbert W. Verfasser aut Quantum gravitation the Feynman path integral approach Herbert W. Hamber Berlin [u.a.] Springer 2009 XVII, 342 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Feynman integrals Quantum gravity Pfadintegral (DE-588)4173973-5 gnd rswk-swf Quantengravitation (DE-588)4124012-1 gnd rswk-swf Quantengravitation (DE-588)4124012-1 s Pfadintegral (DE-588)4173973-5 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016995018&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Hamber, Herbert W. Quantum gravitation the Feynman path integral approach Feynman integrals Quantum gravity Pfadintegral (DE-588)4173973-5 gnd Quantengravitation (DE-588)4124012-1 gnd |
subject_GND | (DE-588)4173973-5 (DE-588)4124012-1 |
title | Quantum gravitation the Feynman path integral approach |
title_auth | Quantum gravitation the Feynman path integral approach |
title_exact_search | Quantum gravitation the Feynman path integral approach |
title_exact_search_txtP | Quantum gravitation the Feynman path integral approach |
title_full | Quantum gravitation the Feynman path integral approach Herbert W. Hamber |
title_fullStr | Quantum gravitation the Feynman path integral approach Herbert W. Hamber |
title_full_unstemmed | Quantum gravitation the Feynman path integral approach Herbert W. Hamber |
title_short | Quantum gravitation |
title_sort | quantum gravitation the feynman path integral approach |
title_sub | the Feynman path integral approach |
topic | Feynman integrals Quantum gravity Pfadintegral (DE-588)4173973-5 gnd Quantengravitation (DE-588)4124012-1 gnd |
topic_facet | Feynman integrals Quantum gravity Pfadintegral Quantengravitation |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016995018&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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