Gravitation et quantifications: 5 juillet - 1 août 1992 = Gravitation and quantizations
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| Format: | Book |
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| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
1995
|
| Series: | École d'Été de Physique Théorique <LesHouches>: Session
57 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zsfassung in franz. Sprache |
| Physical Description: | XXXIII, 950 S. Ill., graph. Darst. |
| ISBN: | 0444820760 |
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| 245 | 1 | 0 | |a Gravitation et quantifications |b 5 juillet - 1 août 1992 = Gravitation and quantizations |c éd. par B. Julia ... |
| 246 | 1 | 1 | |a Gravitation and quantizations |
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 1995 | |
| 300 | |a XXXIII, 950 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a École d'Été de Physique Théorique <LesHouches>: Session |v 57 | |
| 500 | |a Zsfassung in franz. Sprache | ||
| 650 | 0 | 7 | |a Gravitation |0 (DE-588)4021908-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantengravitation |0 (DE-588)4124012-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantisierung |g Physik |0 (DE-588)4176603-9 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |y 1992 |z Les Houches |2 gnd-content | |
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| 700 | 1 | |a Julia, B. |e Sonstige |4 oth | |
| 830 | 0 | |a École d'Été de Physique Théorique <LesHouches>: Session |v 57 |w (DE-604)BV000022608 |9 57 | |
| 856 | 4 | 2 | |m Digitalisierung TU Muenchen |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007016111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007016111 | ||
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| adam_text | CONTENTS
Lecturers
¡x
Participants
x¡
Préface
(French)
xv
Preface (English)
x¡x
PART I. GRAVITATION
Course
1.
Gravitation and experiment, by T. Damour
1
1.
Introduction
5
2.
Methodologies for testing theories
6
2.1.
Phenomenological approach ( compare )
7
2.2.
Theory-space approach ( contrast )
8
3.
Testing what?
11
3.1.
The two structural elements of general relativity
11
3.2.
New, macroscopic fields and couplings
13
4.
Testing the coupling of matter to an external gravitational field
14
4.1.
Experimental consequences of universal metric coupling
14
4.2.
Non-metric couplings and their observational consequences
17
4.2.1.
Dilaton-like couplings
17
4.2.2.
Multi-metric couplings, antisymmetric tensor couplings, and local
Lorentz
invariance
19
4.2.3.
Other couplings of matter to scalar, vector, or tensor fields and their
experimental consequences
22
4.3.
Experimental results on the coupling of matter to an external gravitational
field
24
4.4.
Theoretical conclusions about the coupling of matter to an external gravi¬
tational field
26
xxiii
5.
Testing
the
Newtonian
and post-Newtonian limits of metric theories of gravity
28
5.1.
What are the most natural metric alternatives to Einstein s theory?
28
5.2.
The Newtonian limit of tensor-multi-scalar theories and its experimental
tests
31
5.3.
The post-Newtonian limit of tensor-multi-scalar theories and its experi¬
mental tests
36
5.4.
Theoretical conclusions about weak-field, metric gravity
41
6.
Testing the strong and radiative gravitational field regimes
43
6.1.
Binary pulsars as laboratories for probing strong and radiative gravitational
fields
43
6.2.
Phenomenological analysis of binary-pulsar data ( parametrized post-Keplerian
formalism )
45
6.3.
Theory-space approach to binary-pulsar tests: introduction of strong-field
parameters
faß , ß ,... 47
6.4.
Experimental constraints on strong-field relativistic gravity
50
7.
Other tests and conclusions
53
7.1.
Testing gravity on large scales
53
7.2.
Cosmological tests
54
7.3.
Other astrophysical tests and possible dark clouds
55
7.4.
Tests to come?
55
7.5.
Overall conclusions
56
Appendix
57
References
57
Course
2.
Quantum field theory in curved space-time,
by
RM.
Wald 63
1.
Introduction and preliminaries
67
1.1.
Introduction and overview
67
1.2.
Classical dynamics of particle systems
71
1.3.
Quantum mechanics
74
1.4.
Harmonic oscillators
77
2.
Quantum fields in flat space-time
83
2.1.
Basic construction
83
2.2.
Reformulation
86
2.3.
Particle interpretation
93
3.
Quantum fields in curved space-time
97
3.1.
Curved space-time; global hyperbolicity
97
3.2.
Construction of quantum field theory in curved space-time
99
3.3.
Quantum field theory in stationary space-times
102
3.4.
Unitary equivalence; the S-matrix
105
3.5.
The algebraic approach
110
3.6.
The stress-energy tensor
118
4. The Unruh
effect
129
4.1.
The
Unruh
effect
in flat space-time
129
4.2.
Generalization to curved space-times
138
5.
The Hawking effect
146
5.1.
Particle creation by black holes
146
5.2.
Ramifications
154
Appendix A. Some basic definitions and constructions pertaining to Hubert spaces
160
A.I. Some basic definitions
161
A.
2.
Some basic constructions
162
A3.
Index notation
164
References
166
Seminar
1.
Covariant nonlocal effective action in gauge
theories and quantum gravity,
by A.O. Barvinsky
169
References
172
Seminar
2.
References
The unification of black holes with ordinary
matter, by G.
t Hooft
173
179
Course
3.
Mathematical problems of non-perturbative
quantum general relativity, by A. Ashtekar
181
Introduction
1.1.
The problem
1.2.
Difficulties
1.2.1.
Particle theorist s strategies
1.2.2.
Mathematical physicist s methods
1.2.3.
General relativist s approaches
1.3.
Overview
Mathematical preliminaries
2.1.
Symplectic framework
2.2.
First class constraints
2.3.
Di rac
quantization program and its limitations
2.4.
Algebraic quantization program
2.5.
Connections and loops: a non-linear duality
185
185
188
189
192
194
197
199
200
202
205
208
211
xxv
3.
Three
faces
of
2+1
quantum gravity
216
3.1.
Introduction
216
3.2.
Hamiltonian formulation
218
3.3.
Timeless description: frozen formalism
223
3.4.
Discrete elements: pre-geometry
227
3.5.
Extracting time: dynamics unfolded
229
4. 3+1
General relativity as connection dynamics
233
4.1.
Introduction
233
4.2.
Hamiltonian framework
236
4.3.
Rovelli-Smolin loop variables
242
5.
The loop representation for
3+1
gravity
248
5.1.
Introduction
248
5.2.
The loop representation
251
5.3.
Regularization and weaves
256
5.4.
Quantum dynamics
265
5.5.
Outlook
268
6.
Discussion
272
6.1.
Summary
272
6.2.
Open issues and directions for the future
275
6.3.
An evaluation
279
References
282
Course
4.
Spacetime quantum mechanics and the quantum
mechanics of spacetime, by J.B. Hartle
285
1.
Introduction
289
2.
The quantum mechanics of closed systems
294
2.1.
Quantum mechanics and cosmology
294
2.2.
Probabilities in general and probabilities in quantum mechanics
295
2.3.
Probabilities for a time sequence of measurements
298
2.4.
Post-Everett quantum mechanics
300
2.5.
The origins of decoherence in our universe
307
2.6.
The Copenhagen approximation
310
2.7.
Quasiclassical domains
311
3.
Decoherence in general, decoherence in particular, and the emergence of clas¬
sical behavior
313
3.1.
A more general formulation of the quantum mechanics of closed systems
313
3.1.1.
Fine-grained and coarse-grained histories
314
3.1.2.
The decoherence functional
316
3.1.3.
Prediction, retrodiction, and states
318
3.1.4.
The decoherence functional in path-integral form
320
3.2.
The Emch model
322
xxvi
3.3. Linear
oscillator models
324
3.3.1.
Specification
324
3.3.2.
The influence phase and decoherence
325
3.4.
The emergence of a quasiclassical domain
328
4.
Generalized quantum mechanics
337
4.1.
Three elements
337
4.2.
Hamiltonian quantum mechanics as a generalized quantum mechanics
340
4.3.
Sum-over-histories quantum mechanics for theories with a time
342
4.4.
Differences between and equivalences of Hamiltonian and sum-over-
histories quantum mechanics for theories with a time
344
4.5.
Classical physics and the classical limit of quantum mechanics
346
4.6.
Generalizations of Hamiltonian quantum mechanics
348
4.7.
A time-neutral formulation of quantum mechanics
349
5.
The spacetime approach to non-relativistic quantum mechanics
352
5.1.
A generalized sum-over-histories quantum mechanics for non-relativistic
systems
352
5.2.
Evaluating path integrals
358
5.2.1.
Product formulae
358
5.2.2.
Phase-space path integrals
360
5.3.
Examples of coarse grainings
361
5.3.1.
Alternatives at definite moments of time
361
5.3.2.
Alternatives defined by a spacetime region
363
5.3.3.
A simple example of a decoherent spacetime coarse graining
365
5.4.
Coarse grainings by functional of the paths
367
5.4.1.
General coarse grainings
367
5.4.2.
Coarse grainings defining momentum
369
5.5.
The relation between the Hamiltonian and generalized sum-over-histories
formulations of non-relativistic quantum mechanics
371
6.
Abelian gauge theories
373
6.1.
Gauge and reparametrization
invariance
373
6.2.
Coarse grainings of the electromagnetic field
375
6.3.
Specific examples
379
6.4.
Constraints
380
6.5.
ADM and Dirac quantization
383
7.
Models with a single reparametrization
invariance
387
7.1.
Reparametrization
invariance
in general
387
7.2.
Constraints and path integrals
391
7.3.
Parametrized non-relativistic quantum mechanics
395
7.4.
The relativistic world line
-
formulation with a preferred time
400
7.5.
The relativistic world line
-
formulation without a preferred time
403
7.5.1.
Fine-grained histories, coarse grainings, and decoherence func¬
tional
403
7.5.2.
Explicit examples
409
7.5.3.
Connection with field theory
411
7.5.4.
No equivalent Hamiltonian formulation
413
7.5.5.
The probability of the constraint
414
7.6.
Relation to Dirac quantization
416
8.
General relativity
420
8.1.
General relativity and quantum gravity
420
8.2.
Fine-grained histories of metric and fields and their simplicial approxi¬
mation
422
8.3.
Coarse grainings of spacetime
425
8.4.
The decoherence functional for general relativity
429
8.4.1.
Actions,
invariance,
constraints
430
8.4.2.
Class operators
434
8.4.3.
Adjoining initial and final conditions
437
8.5.
Discussion
-
the problem of time
442
8.6.
Discussion
-
constraints
444
8.7.
Simplicial models
447
8.8.
Initial and final conditions in quantum cosmology
451
9.
Semiclassical predictions
453
9.1.
The semiclassical regime
453
9.2.
The semiclassical approximation to the quantum mechanics of a non-
relativistic particle
454
9.3.
The semiclassical approximation for the relativistic particle
458
9.4.
The approximation of field theory in semiclassical spacetime
462
9.5.
Rules for semiclassical prediction and the emergence of Hamiltonian
quantum mechanics
467
10.
Summary
469
Appendix A. Notation and conventions
474
References
475
PART
П.
QUANTUM MODELS
Course
5.
Topics in string theory and quantum gravity,
by L.
Alvarez-Gaumé
and MA.
Vázquez-Mozo
481
0.
General introduction
485
1.
Field-theoretical approach to quantum gravity
488
1.1.
Linearized gravity
489
1.2.
Supergravity
490
1.3.
Kaluza-Klein theories
492
1.4.
Quantum field theory and classical gravity
495
1.5.
Euclidean approach to quantum gravity
503
xxvui
1.6.
Canonical quantization of gravity
508
1.7.
Gravitational
instantons
510
2.
Consistency conditions: anomalies
512
2.1.
Generalities about anomalies
512
2.2.
Spinors in 2n dimensions
515
2.3.
When can we expect to find anomalies?
519
2.4.
The Atiyah-Singer index theorem and the computation of anomalies
524
2.5.
Examples: Green-Schwarz cancellation mechanism and Witten s SU(2)
global anomaly
539
3.
String theory I. Bosonic strings
542
3.1.
Bosonic string
544
3.2.
Conformai
field theory
552
3.3.
Quantization of the bosonic string
561
3.4.
Interactions in string theory and the characterization of the moduli space
563
3.5.
Bosonic strings with background fields. Stringy corrections to the Ein¬
stein equations
569
3.6.
Toroidal compactifications. n-duality
571
3.7.
Operator formalism
574
4.
String theory II. Fermionic strings
598
4.1.
Fermionic string
598
4.2.
Heterotic string
613
4.3.
Strings at finite temperature
616
4.4.
Is string theory finite?
623
5.
Other developments and conclusions
625
5.1.
String phenomenology
625
5.2.
Black holes and related subjects
627
References
629
Seminar
3.
Solvable extensions of two-dimensional gravity,
by P. van Nieuwenhuizen
637
1.
Introduction
639
2.
Chiral Yang-Mills theory
640
3.
W3 gravity
642
References
645
Course
6.
Closed-string field theory: an introduction,
by B.
Zwieback 647
1.
The origin of the string field
651
2.
String diagrams from an extremal problem
655
2.1.
Two useful results
657
2.2.
The minimal-area problem for closed-string theory
659
2.3.
Why minimal-area metrics work
661
3.
Batalin-Vilkovisky structures
664
3.1.
Symplectic vector spaces
664
3.2.
Ghost
conformai
field theory
666
3.3.
Symplectic structure on Hcft
667
3.3.1.
Reflector state
667
3.3.2.
A kinetic term for closed-string fields
668
3.3.3.
Symplectic structure in
^cft
^71
3.3.4.
BV
structure in space-time
671
4.
Recent developments
672
References
677
Course
7.
Simplicial quantum gravity and random lattices,
by F. David
679
1.
Introduction
683
2.
Piecewise flat manifolds,
Regge
calculus, and dynamical
triangulations
685
2.1.
Simplicial manifolds and piecewise linear spaces
685
2.2.
The dual complex and volume elements
688
2.3.
Spin connection, spinors
689
2.4.
Curvature and the
Regge
action (classical
Regge
calculus)
690
2.5.
Topological invariants
691
2.6.
Simplicial Euclidean quantum gravity (quantum
Regge
calculus)
692
2.7.
Dynamical
triangulations
(DT)
693
3.
Two-dimensional gravity, dynamical
triangulations,
and matrix models
695
3.1.
Continuum formulation of 2D gravity
696
3.2.
Dynamical
triangulations
and continuum limit
700
3.3.
The one-matrix model
703
3.4.
Various matrix models
706
3.4.1.
General potential
706
3.4.2.
Symmetric matrix model
707
3.4.3.
Multi-matrix models
708
3.4.4.
d-Dimensional bosonic string
709
3.5.
Numerical studies of 2D gravity
711
3.5.1.
Series expansions
711
3.5.2.
Monte Carlo simulations
712
3.5.3.
Sampling methods using exact results
714
3.5.4.
2D quantum
Regge
calculus
714
xxx
3.6.
Thec=
1
barrier
715
3.6.1.
Surfaces versus branched polymers
715
3.6.2.
Tachyons for the bosonic string
716
3.6.3.
Spikes/wormholes picture
717
3.6.4.
Numerical studies of the
с
> 1
phase
718
3.7.
Intrinsic geometry of 2D gravity
720
3.8.
Liouville theory at
с
> 25 722
4.
Euclidean quantum gravity at
D
> 2 723
4.1.
What are we looking for?
723
4.2.
Simplicial
3D
gravity
725
4.3.
Simplicial 4D gravity
729
4.4. 3D
and 4D quantum
Regge
calculus
730
5.
Non-perturbative problems in 2D quantum gravity
730
5.1.
The continuum double-scaling limit
730
5.2.
The
Painlevé
I string equation
733
5.3.
Non-perturbative properties of the string equation
735
5.4.
Divergent series and
Borei summability
738
5.5.
Non-perturbative effects in 2D gravity and string theories
741
5.6.
Various stabilization proposals
743
5.6.1.
Stochastic quantization
744
5.6.2.
Complex matrix models
745
5.6.3.
Complex solutions
745
6.
Conclusion
746
References
746
Course
8.
Matrix models of two-dimensional quantum
gravity, by E.
Brezin
751
1.
Discretized strings and matrix models
755
2.
Scaling laws
757
3.
Matrix integrals in the
large
-ЛГ
planar limit
759
4.
Beyond the planar limit: recursion formulae
763
5.
String equations for one-matrix models
765
6.
Correlation functions
769
7.
Multi-matrix models
771
8.
The
с
= 1
string and free
fermions
774
9.
Beyond
с
= 1 779
References
780
Course
9.
A few projects in string theory, by A.M. Polyakov
783
1.
Introduction
787
xxxi
2.
Quantum
gravity
787
3.
Phases in gravity
789
4.
Self-tuning universe
790
5.
The
dilaten
792
6.
The Big Bang
793
7.
Fuzzy strings and
3D
Ising model
795
8.
The QCD string
798
9.
Scale dependence in quantum gravity
800
10.
Conclusions
803
References
804
Course
10.
Non-commutative geometry and physics,
by A. Connes
805
Introduction
809
1.
The
involuti ve
algebra of coordinates on a quantum space X
816
2.
Measure theory and representations
827
2.1.
The GNS construction
828
2.2.
The commutative case
830
2.3.
The modular theory
831
2.4.
The classification of factors
834
2.5.
The KMS condition and quantum-statistical mechanics
835
3.
C*-algebras and topology
838
4.
Vector bundles and cyclic cohomology
847
4.1.
The Gauss-Bonnet theorem
847
4.2.
Vector bundles and idempotents
849
4.3.
Invariants of vector bundles
851
4.4.
Vector bundles over quantum spaces
853
4.5.
ЙГ
-theory
854
4.6.
Cyclic cohomology
856
5.
The quantized calculus
862
5.1.
Example
1: ƒ
f(Z) dZ p
868
5.1.1.
Hausdorff measure and the Caratheodory construction
873
5.2.
Example
2:
¡EdEdEeZ
876
5.3.
Example
3:
the trace of the metric
881
6.
The metric aspect and classical matter fields
892
6.1.
Riemannian manifolds and the Dirac operator
894
6.2.
Product of continuum and discrete, and the symmetry breaking mechanism
908
6.2.1.
Example (a): two-point space
910
6.2.2.
Example (b): (four-dimensional Riemannian manifold
Μ) χ
(two-
point space X)
915
xxxii
7.
The notion of manifold in non-commutative geometry
925
7.1.
The classical notion of manifold
925
7.2.
The
KO
orientation of a manifold
926
7.3.
Fredholm
modules and K-homology
928
7.4.
Poincaré
duality in
.řf-homology
and non-commutative C*-algebras
929
7.5.
Non-commutative manifolds
932
8.
Geometric interpretation of the standard model
933
8.1.
The standard model
934
8.2.
Geometric structure of the finite space
F
937
8.3.
Geometric structure of the standard model
941
8.4.
Unimodularity condition and hypercharges
945
References
948
xxxiii
|
| any_adam_object | 1 |
| building | Verbundindex |
| bvnumber | BV010526723 |
| classification_rvk | UH 8500 |
| classification_tum | PHY 044f |
| ctrlnum | (OCoLC)645821561 (DE-599)BVBBV010526723 |
| discipline | Physik |
| format | Book |
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| genre | (DE-588)1071861417 Konferenzschrift 1992 Les Houches gnd-content |
| genre_facet | Konferenzschrift 1992 Les Houches |
| id | DE-604.BV010526723 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:54:30Z |
| institution | BVB |
| isbn | 0444820760 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007016111 |
| oclc_num | 645821561 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-703 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-703 |
| physical | XXXIII, 950 S. Ill., graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Elsevier |
| record_format | marc |
| series | École d'Été de Physique Théorique <LesHouches>: Session |
| series2 | École d'Été de Physique Théorique <LesHouches>: Session |
| spelling | Gravitation et quantifications 5 juillet - 1 août 1992 = Gravitation and quantizations éd. par B. Julia ... Gravitation and quantizations Amsterdam [u.a.] Elsevier 1995 XXXIII, 950 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier École d'Été de Physique Théorique <LesHouches>: Session 57 Zsfassung in franz. Sprache Gravitation (DE-588)4021908-2 gnd rswk-swf Quantengravitation (DE-588)4124012-1 gnd rswk-swf Quantisierung Physik (DE-588)4176603-9 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1992 Les Houches gnd-content Quantisierung Physik (DE-588)4176603-9 s DE-604 Gravitation (DE-588)4021908-2 s Quantengravitation (DE-588)4124012-1 s Julia, B. Sonstige oth École d'Été de Physique Théorique <LesHouches>: Session 57 (DE-604)BV000022608 57 Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007016111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gravitation et quantifications 5 juillet - 1 août 1992 = Gravitation and quantizations École d'Été de Physique Théorique <LesHouches>: Session Gravitation (DE-588)4021908-2 gnd Quantengravitation (DE-588)4124012-1 gnd Quantisierung Physik (DE-588)4176603-9 gnd |
| subject_GND | (DE-588)4021908-2 (DE-588)4124012-1 (DE-588)4176603-9 (DE-588)1071861417 |
| title | Gravitation et quantifications 5 juillet - 1 août 1992 = Gravitation and quantizations |
| title_alt | Gravitation and quantizations |
| title_auth | Gravitation et quantifications 5 juillet - 1 août 1992 = Gravitation and quantizations |
| title_exact_search | Gravitation et quantifications 5 juillet - 1 août 1992 = Gravitation and quantizations |
| title_full | Gravitation et quantifications 5 juillet - 1 août 1992 = Gravitation and quantizations éd. par B. Julia ... |
| title_fullStr | Gravitation et quantifications 5 juillet - 1 août 1992 = Gravitation and quantizations éd. par B. Julia ... |
| title_full_unstemmed | Gravitation et quantifications 5 juillet - 1 août 1992 = Gravitation and quantizations éd. par B. Julia ... |
| title_short | Gravitation et quantifications |
| title_sort | gravitation et quantifications 5 juillet 1 aout 1992 gravitation and quantizations |
| title_sub | 5 juillet - 1 août 1992 = Gravitation and quantizations |
| topic | Gravitation (DE-588)4021908-2 gnd Quantengravitation (DE-588)4124012-1 gnd Quantisierung Physik (DE-588)4176603-9 gnd |
| topic_facet | Gravitation Quantengravitation Quantisierung Physik Konferenzschrift 1992 Les Houches |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007016111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022608 |
| work_keys_str_mv | AT juliab gravitationetquantifications5juillet1aout1992gravitationandquantizations AT juliab gravitationandquantizations |