Modern canonical quantum general relativity:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge monographs on mathematical physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXVI, 819 S. Ill., graph. Darst. |
| ISBN: | 9780521842631 0521842638 |
Internformat
MARC
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| 020 | |a 9780521842631 |c (hbk) |9 978-0-521-84263-1 | ||
| 020 | |a 0521842638 |9 0-521-84263-8 | ||
| 035 | |a (OCoLC)255621587 | ||
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| 084 | |a UH 8300 |0 (DE-625)145781: |2 rvk | ||
| 100 | 1 | |a Thiemann, Thomas |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Modern canonical quantum general relativity |c Thomas Thiemann |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
| 300 | |a XXVI, 819 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Cambridge monographs on mathematical physics | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a General relativity (Physics) | |
| 650 | 4 | |a Quantum theory | |
| 650 | 0 | 7 | |a Quantentheorie |0 (DE-588)4047992-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Allgemeine Relativitätstheorie |0 (DE-588)4112491-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Allgemeine Relativitätstheorie |0 (DE-588)4112491-1 |D s |
| 689 | 0 | 1 | |a Quantentheorie |0 (DE-588)4047992-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016068087&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016068087 | ||
Datensatz im Suchindex
| _version_ | 1804137117675159552 |
|---|---|
| adam_text | Contents
Foreword, by Chris Isham page
xvii
Preface
xix
Notation and conventions
xxiii
Introduction: Defining quantum gravity
1
Why quantum gravity in the twenty-first century?
1
The role of background independence
8
Approaches to quantum gravity
11
Motivation for canonical quantum general relativity
23
Outline of the book
25
I CLASSICAL FOUNDATIONS, INTERPRETATION AND THE
CANONICAL QUANTISATION PROGRAMME
1
Classical Hamiltonian formulation of General Relativity
39
1.1
The ADM action
39
1.2
Legendre transform and Dirac analysis of constraints
46
1.3
Geometrical interpretation of the gauge transformations
50
1.4
Relation between the four-dimensional diffeomorphism group and
the transformations generated by the constraints
56
1.5
Boundary conditions, gauge transformations and symmetries
60
1.5.1
Boundary conditions
60
1.5.2
Symmetries and gauge transformations
65
2
The problem of time, locality and the interpretation of
quantum mechanics
74
2.1
The classical problem of time: Dirac
observables
75
2.2
Partial and complete
observables
for general constrained systems
81
2.2.1
Partial and weak complete
observables
82
2.2.2
Poisson
algebra of Dirac
observables
85
2.2.3
Evolving constants
89
2.2.4
Reduced phase space quantisation of the algebra of Dirac
observables
and unitary implementation of the
multi-fingered time evolution
90
2.3
Recovery of locality in General Relativity
93
x
Contents
2.4 Quantum
problem
of time: physical inner product and
interpretation of quantum mechanics
95
2.4.1
Physical inner product
95
2.4.2
Interpretation of quantum mechanics
98
3
The programme of canonical quantisation
107
3.1
The programme
108
4
The new canonical variables of Ashtekar for
General Relativity
118
4.1
Historical overview
118
4.2
Derivation of Ashtekar s variables
123
4.2.1
Extension of the ADM phase space
123
4.2.2
Canonical transformation on the extended phase space
126
II FOUNDATIONS OF MODERN CANONICAL QUANTUM
GENERAL RELATIVITY
5
Introduction
141
5.1
Outline and historical overview
141
6
Step I: the holonomy-flux algebra
φ
157
6.1
Motivation for the choice of
φ
157
6.2
Definition of
φ:
(1)
Paths, connections, holonomies and
cylindrical functions
162
6.2.1
Semianalytic paths and holonomies
162
6.2.2
A natural topology on the space of generalised connections
168
6.2.3
Gauge
invariance:
distributional gauge transformations
175
6.2.4
The C* algebraic viewpoint and cylindrical functions
183
6.3
Definition of
φ:
(2)
surfaces, electric fields, fluxes and vector fields
191
6.4
Definition of
φ:
(3)
régularisation
of the holonomy-flux
Poisson
algebra
194
6.5
Definition of
φ:
(4)
Lie algebra of cylindrical functions and
flux vector fields
202
7
Step II: quantum *-algebra
21 206
7.1
Definition of
21 206
7.2
(Generalised) bundle automorphisms of
21 209
8
Step III: representation theory of
21 212
8.1
General considerations
212
8.2
Uniqueness proof:
(1)
existence
219
8.2.1
Regular
Borei
measures on the
projective
limit:
the uniform measure
220
8.2.2
Functional calculus on
a projective
limit
226
Contents xi
8.2.3 +
Density and support properties of A,
А/С
with respect
to
à Ã/Q
233
8.2.4
Spin-network functions and loop representation
237
8.2.5
Gauge and diffeomorphism
invariance
of
μο
242
8.2.6
+ Ergodicity of
μο
with respect to spatial diffeomorphisms
245
8.2.7
Essential self-adjointness of electric flux momentum
operators
246
8.3
Uniqueness proof:
(2)
uniqueness
247
8.4
Uniqueness proof:
(3)
irreducibility
252
9
Step IV:
(1)
implementation and solution of the
kinematical constraints
264
9.1
Implementation of the
Gauß
constraint
264
9.1.1
Derivation of the
Gauß
constraint operator
264
9.1.2
Complete solution of the
Gauß
constraint
266
9.2
Implementation of the spatial diffeomorphism constraint
269
9.2.1
Derivation of the spatial diffeomorphism constraint
operator
269
9.2.2
General solution of the spatial diffeomorphism constraint
271
10
Step IV:
(2)
implementation and solution of the
Hamiltonian constraint
279
10.1
Outline of the construction
279
10.2
Heuristic explanation for UV finiteness due to background
independence
282
10.3
Derivation of the Hamiltonian constraint operator
286
10.4
Mathematical definition of the Hamiltonian constraint operator
291
10.4.1
Concrete implementation
291
10.4.2
Operator limits
296
10.4.3
Commutator algebra
300
10.4.4
The quantum Dirac algebra
309
10.5
The kernel of the Wheeler-DeWitt constraint operator
311
10.6
The Master Constraint Programme
317
10.6.1
Motivation for the Master Constraint Programme in
General Relativity
317
10.6.2
Definition of the Master Constraint
320
10.6.3
Physical inner product and Dirac
observables
326
10.6.4
Extended Master Constraint
329
10.6.5
Algebraic Quantum Gravity (AQGj
331
10.7 +
Further related results
334
10.7.1
The Wick transform
334
10.7.2
Testing the new
régularisation
technique by models of
quantum gravity
340
xii Contents
10.7.3 Quantum
Poincaré algebra
341
10.7.4 Vasiliev
invariants
and discrete quantum gravity
344
11
Step V: semiclassical analysis
345
11.1 +
Weaves
349
11.2
Coherent states
353
11.2.1
Semiclassical states and coherent states
354
11.2.2
Construction principle: the complexifier method
356
11.2.3
Complexifier coherent states for diffeomorphism-invariant
theories of connections
362
11.2.4
Concrete example of complexifier
367
11.2.5
Semiclassical limit of loop quantum gravity: graph-changing
operators, shadows and diffeomorphism-invariant
coherent states
376
11.2.6
+ The infinite tensor product extension
385
11.3
Graviton and photon Fock states from L2
(.Α, ψο)
390
III PHYSICAL APPLICATIONS
12
Extension to standard matter
399
12.1
The classical standard model coupled to gravity
400
12.1.1
Fermionic and Einstein contribution
401
12.1.2
Yang-Mills and Higgs contribution
405
12.2
Kinematical Hubert spaces for diffeomorphism-invariant theories
of fermion and Higgs fields
406
12.2.1
Fermionic sector
406
12.2.2
Higgs sector
411
12.2.3
Gauge and diffeomorphism-invariant subspace
417
12.3
Quantisation of matter Hamiltonian constraints
418
12.3.1
Quantisation of Einstein-Yang-Mills theory
419
12.3.2
Fermionic sector
422
12.3.3
Higgs sector
425
12.3.4
A general quantisation scheme
429
13
Kinematical geometrical operators
431
13.1
Derivation of the area operator
432
13.2
Properties of the area operator
434
13.3
Derivation of the volume operator
438
13.4
Properties of the volume operator
447
13.4.1
Cylindrical consistency
447
13.4.2
Symmetry,
positivity
and self-adjoint ness
448
13.4.3
Discreteness and anomaly-freeness
448
13.4.4
Matrix elements
44g
13.5
Uniqueness of the volume operator, consistency with the flux
operator and pseudo-two-forms
453
Contents xiii
13.6
Spatially diffeomorphism-invariant volume operator
455
14
Spin foam models
458
14.1
Heuristic motivation from the canonical framework
458
14.2
Spin foam models from BF theory
462
14.3
The Barrett-Crane model
466
14.3.1
Plebański
action and simplicity constraints
466
14.3.2
Discretisation theory
472
14.3.3
Discretisation and quantisation of BF theory
476
14.3.4
Imposing the simplicity constraints
482
14.3.5
Summary of the status of the Barrett-Crane model
494
14.4 Triangulation
dependence and group field theory
495
14.5
Discussion
502
15
Quantum black hole physics
511
15.1
Classical preparations
514
15.1.1
Null geodesic congruences
514
15.1.2
Event horizons, trapped surfaces and apparent horizons
517
15.1.3
Trapping, dynamical, non-expanding and (weakly) isolated
horizons
519
15.1.4
Spherically symmetric isolated horizons
526
15.1.5
Boundary symplectic structure for SSIHs
535
15.2
Quantisation of the surface degrees of freedom
540
15.2.1
Quantum U(l) Chern-Simons theory with punctures
541
15.3
Implementing the quantum boundary condition
546
15.4
Implementation of the quantum constraints
548
15.4.1
Remaining U(l) gauge transformations
549
15.4.2
Remaining surface diffeomorphism transformations
550
15.4.3
Final physical Hubert space
550
15.5
Entropy counting
550
15.6
Discussion
557
16
Applications to particle physics and quantum cosmology
562
16.1
Quantum gauge fixing
562
16.2
Loop Quantum Cosmology
563
17
Loop Quantum Gravity phenomenology
572
IV MATHEMATICAL TOOLS AND THEIR CONNECTION
TO PHYSICS
18
Tools from general topology
577
18.1
Generalities
577
18.2
Specific results
581
xiv
Contents
19
Differential, Riemannian, symplectic and complex
geometry
585
19.1
Differential geometry
585
19.1.1
Manifolds
585
19.1.2
Passive and active diffeomorphisras
587
19.1.3
Differential calculus
590
19.2
Riemannian geometry
606
19.3
Symplectic manifolds
614
19.3.1
Symplectic geometry
614
19.3.2
Symplectic reduction
616
19.3.3
Symplectic group actions
621
19.4
Complex, Hermitian and
Kahler
manifolds
623
20
Semianalytic category
627
20.1
Semianalytic structures on K™
627
20.2
Semianalytic manifolds and submanifolds
631
21
Elements of fibre bundle theory
634
21.1
General fibre bundles and principal fibre bundles
634
21.2
Connections on principal fibre bundles
636
22
Holonomies on non-trivial fibre bundles
644
22.1
The groupoid of equivariant maps
644
22.2
Holonomies and transition functions
647
23
Geometric quantisation
652
23.1
Prequantisation
652
23.2
Polarisation
662
23.3
Quantisation
668
24
The Dirac algorithm for field theories with constraints
671
24.1
The Dirac algorithm
671
24.2
First- and second-class constraints and the Dirac bracket
674
25
Tools from measure theory
680
25.1
Generalities and the Riesz-Markov theorem
680
25.2
Measure theory and ergodicity
687
26
Key results from functional analysis
26.1
Metric spaces and normed spaces
689
689
26.2
Hubert spaces
59]
26.3
Banach spaces
593
26.4
Topological spaces g94
26.5
Locally convex spaces
594
26.6
Bounded operators
595
26.7
Unbounded operators
Contents xv
26.8
Quadratic forms
699
27
Elementary introduction to Gel fand theory for
Abelian C*-algebras
701
27.1
Banach algebras and their spectra
701
27.2
The Gel fand transform and the Gel fand isomorphism
709
28
Bohr compactification of the real line
713
28.1
Definition and properties
713
28.2
Analogy with loop quantum gravity
715
29
Operator -algebras and spectral theorem
719
29.1
Operator *-algebras, representations and GNS construction
719
29.2
Spectral theorem, spectral measures, projection valued measures,
functional calculus
723
30
Refined algebraic quantisation (RAQ) and direct integral
decomposition (DID)
729
30.1
RAQ
729
30.2
Master Constraint Programme (MCP) and DID
735
31
Basics of harmonic analysis on compact Lie groups
746
31.1
Representations and
Haar
measures
746
31.2
The Peter and Weyl theorem
752
32
Spin-network functions for SU(2)
755
32.1
Basics of the representation theory of
SU
(2) 755
32.2
Spin-network functions and recoupling theory
757
32.3
Action of holonomy operators on spin-network functions
762
32.4
Examples of coherent state calculations
765
33
+ Functional analytic description of classical connection
dynamics
770
33.1
Infinite-dimensional (symplectic) manifolds
770
References
775
Index
809
|
| adam_txt |
Contents
Foreword, by Chris Isham page
xvii
Preface
xix
Notation and conventions
xxiii
Introduction: Defining quantum gravity
1
Why quantum gravity in the twenty-first century?
1
The role of background independence
8
Approaches to quantum gravity
11
Motivation for canonical quantum general relativity
23
Outline of the book
25
I CLASSICAL FOUNDATIONS, INTERPRETATION AND THE
CANONICAL QUANTISATION PROGRAMME
1
Classical Hamiltonian formulation of General Relativity
39
1.1
The ADM action
39
1.2
Legendre transform and Dirac analysis of constraints
46
1.3
Geometrical interpretation of the gauge transformations
50
1.4
Relation between the four-dimensional diffeomorphism group and
the transformations generated by the constraints
56
1.5
Boundary conditions, gauge transformations and symmetries
60
1.5.1
Boundary conditions
60
1.5.2
Symmetries and gauge transformations
65
2
The problem of time, locality and the interpretation of
quantum mechanics
74
2.1
The classical problem of time: Dirac
observables
75
2.2
Partial and complete
observables
for general constrained systems
81
2.2.1
Partial and weak complete
observables
82
2.2.2
Poisson
algebra of Dirac
observables
85
2.2.3
Evolving constants
89
2.2.4
Reduced phase space quantisation of the algebra of Dirac
observables
and unitary implementation of the
multi-fingered time evolution
90
2.3
Recovery of locality in General Relativity
93
x
Contents
2.4 Quantum
problem
of time: physical inner product and
interpretation of quantum mechanics
95
2.4.1
Physical inner product
95
2.4.2
Interpretation of quantum mechanics
98
3
The programme of canonical quantisation
107
3.1
The programme
108
4
The new canonical variables of Ashtekar for
General Relativity
118
4.1
Historical overview
118
4.2
Derivation of Ashtekar's variables
123
4.2.1
Extension of the ADM phase space
123
4.2.2
Canonical transformation on the extended phase space
126
II FOUNDATIONS OF MODERN CANONICAL QUANTUM
GENERAL RELATIVITY
5
Introduction
141
5.1
Outline and historical overview
141
6
Step I: the holonomy-flux algebra
φ
157
6.1
Motivation for the choice of
φ
157
6.2
Definition of
φ:
(1)
Paths, connections, holonomies and
cylindrical functions
162
6.2.1
Semianalytic paths and holonomies
162
6.2.2
A natural topology on the space of generalised connections
168
6.2.3
Gauge
invariance:
distributional gauge transformations
175
6.2.4
The C* algebraic viewpoint and cylindrical functions
183
6.3
Definition of
φ:
(2)
surfaces, electric fields, fluxes and vector fields
191
6.4
Definition of
φ:
(3)
régularisation
of the holonomy-flux
Poisson
algebra
194
6.5
Definition of
φ:
(4)
Lie algebra of cylindrical functions and
flux vector fields
202
7
Step II: quantum *-algebra
21 206
7.1
Definition of
21 206
7.2
(Generalised) bundle automorphisms of
21 209
8
Step III: representation theory of
21 212
8.1
General considerations
212
8.2
Uniqueness proof:
(1)
existence
219
8.2.1
Regular
Borei
measures on the
projective
limit:
the uniform measure
220
8.2.2
Functional calculus on
a projective
limit
226
Contents xi
8.2.3 +
Density and support properties of A,
А/С
with respect
to
à "Ã/Q
233
8.2.4
Spin-network functions and loop representation
237
8.2.5
Gauge and diffeomorphism
invariance
of
μο
242
8.2.6
+ Ergodicity of
μο
with respect to spatial diffeomorphisms
245
8.2.7
Essential self-adjointness of electric flux momentum
operators
246
8.3
Uniqueness proof:
(2)
uniqueness
247
8.4
Uniqueness proof:
(3)
irreducibility
252
9
Step IV:
(1)
implementation and solution of the
kinematical constraints
264
9.1
Implementation of the
Gauß
constraint
264
9.1.1
Derivation of the
Gauß
constraint operator
264
9.1.2
Complete solution of the
Gauß
constraint
266
9.2
Implementation of the spatial diffeomorphism constraint
269
9.2.1
Derivation of the spatial diffeomorphism constraint
operator
269
9.2.2
General solution of the spatial diffeomorphism constraint
271
10
Step IV:
(2)
implementation and solution of the
Hamiltonian constraint
279
10.1
Outline of the construction
279
10.2
Heuristic explanation for UV finiteness due to background
independence
282
10.3
Derivation of the Hamiltonian constraint operator
286
10.4
Mathematical definition of the Hamiltonian constraint operator
291
10.4.1
Concrete implementation
291
10.4.2
Operator limits
296
10.4.3
Commutator algebra
300
10.4.4
The quantum Dirac algebra
309
10.5
The kernel of the Wheeler-DeWitt constraint operator
311
10.6
The Master Constraint Programme
317
10.6.1
Motivation for the Master Constraint Programme in
General Relativity
317
10.6.2
Definition of the Master Constraint
320
10.6.3
Physical inner product and Dirac
observables
326
10.6.4
Extended Master Constraint
329
10.6.5
Algebraic Quantum Gravity (AQGj
331
10.7 +
Further related results
334
10.7.1
The Wick transform
334
10.7.2
Testing the new
régularisation
technique by models of
quantum gravity
340
xii Contents
10.7.3 Quantum
Poincaré algebra
341
10.7.4 Vasiliev
invariants
and discrete quantum gravity
344
11
Step V: semiclassical analysis
345
11.1 +
Weaves
349
11.2
Coherent states
353
11.2.1
Semiclassical states and coherent states
354
11.2.2
Construction principle: the complexifier method
356
11.2.3
Complexifier coherent states for diffeomorphism-invariant
theories of connections
362
11.2.4
Concrete example of complexifier
367
11.2.5
Semiclassical limit of loop quantum gravity: graph-changing
operators, shadows and diffeomorphism-invariant
coherent states
376
11.2.6
+ The infinite tensor product extension
385
11.3
Graviton and photon Fock states from L2
(.Α, ψο)
390
III PHYSICAL APPLICATIONS
12
Extension to standard matter
399
12.1
The classical standard model coupled to gravity
400
12.1.1
Fermionic and Einstein contribution
401
12.1.2
Yang-Mills and Higgs contribution
405
12.2
Kinematical Hubert spaces for diffeomorphism-invariant theories
of fermion and Higgs fields
406
12.2.1
Fermionic sector
406
12.2.2
Higgs sector
411
12.2.3
Gauge and diffeomorphism-invariant subspace
417
12.3
Quantisation of matter Hamiltonian constraints
418
12.3.1
Quantisation of Einstein-Yang-Mills theory
419
12.3.2
Fermionic sector
422
12.3.3
Higgs sector
425
12.3.4
A general quantisation scheme
429
13
Kinematical geometrical operators
431
13.1
Derivation of the area operator
432
13.2
Properties of the area operator
434
13.3
Derivation of the volume operator
438
13.4
Properties of the volume operator
447
13.4.1
Cylindrical consistency
447
13.4.2
Symmetry,
positivity
and self-adjoint ness
448
13.4.3
Discreteness and anomaly-freeness
448
13.4.4
Matrix elements
44g
13.5
Uniqueness of the volume operator, consistency with the flux
operator and pseudo-two-forms
453
Contents xiii
13.6
Spatially diffeomorphism-invariant volume operator
455
14
Spin foam models
458
14.1
Heuristic motivation from the canonical framework
458
14.2
Spin foam models from BF theory
462
14.3
The Barrett-Crane model
466
14.3.1
Plebański
action and simplicity constraints
466
14.3.2
Discretisation theory
472
14.3.3
Discretisation and quantisation of BF theory
476
14.3.4
Imposing the simplicity constraints
482
14.3.5
Summary of the status of the Barrett-Crane model
494
14.4 Triangulation
dependence and group field theory
495
14.5
Discussion
502
15
Quantum black hole physics
511
15.1
Classical preparations
514
15.1.1
Null geodesic congruences
514
15.1.2
Event horizons, trapped surfaces and apparent horizons
517
15.1.3
Trapping, dynamical, non-expanding and (weakly) isolated
horizons
519
15.1.4
Spherically symmetric isolated horizons
526
15.1.5
Boundary symplectic structure for SSIHs
535
15.2
Quantisation of the surface degrees of freedom
540
15.2.1
Quantum U(l) Chern-Simons theory with punctures
541
15.3
Implementing the quantum boundary condition
546
15.4
Implementation of the quantum constraints
548
15.4.1
Remaining U(l) gauge transformations
549
15.4.2
Remaining surface diffeomorphism transformations
550
15.4.3
Final physical Hubert space
550
15.5
Entropy counting
550
15.6
Discussion
557
16
Applications to particle physics and quantum cosmology
562
16.1
Quantum gauge fixing
562
16.2
Loop Quantum Cosmology
563
17
Loop Quantum Gravity phenomenology
572
IV MATHEMATICAL TOOLS AND THEIR CONNECTION
TO PHYSICS
18
Tools from general topology
577
18.1
Generalities
577
18.2
Specific results
581
xiv
Contents
19
Differential, Riemannian, symplectic and complex
geometry
585
19.1
Differential geometry
585
19.1.1
Manifolds
585
19.1.2
Passive and active diffeomorphisras
587
19.1.3
Differential calculus
590
19.2
Riemannian geometry
606
19.3
Symplectic manifolds
614
19.3.1
Symplectic geometry
614
19.3.2
Symplectic reduction
616
19.3.3
Symplectic group actions
621
19.4
Complex, Hermitian and
Kahler
manifolds
623
20
Semianalytic category
627
20.1
Semianalytic structures on K™
627
20.2
Semianalytic manifolds and submanifolds
631
21
Elements of fibre bundle theory
634
21.1
General fibre bundles and principal fibre bundles
634
21.2
Connections on principal fibre bundles
636
22
Holonomies on non-trivial fibre bundles
644
22.1
The groupoid of equivariant maps
644
22.2
Holonomies and transition functions
647
23
Geometric quantisation
652
23.1
Prequantisation
652
23.2
Polarisation
662
23.3
Quantisation
668
24
The Dirac algorithm for field theories with constraints
671
24.1
The Dirac algorithm
671
24.2
First- and second-class constraints and the Dirac bracket
674
25
Tools from measure theory
680
25.1
Generalities and the Riesz-Markov theorem
680
25.2
Measure theory and ergodicity
687
26
Key results from functional analysis
26.1
Metric spaces and normed spaces
689
689
26.2
Hubert spaces
59]
26.3
Banach spaces
593
26.4
Topological spaces g94
26.5
Locally convex spaces
594
26.6
Bounded operators
595
26.7
Unbounded operators
Contents xv
26.8
Quadratic forms
699
27
Elementary introduction to Gel'fand theory for
Abelian C*-algebras
701
27.1
Banach algebras and their spectra
701
27.2
The Gel'fand transform and the Gel'fand isomorphism
709
28
Bohr compactification of the real line
713
28.1
Definition and properties
713
28.2
Analogy with loop quantum gravity
715
29
Operator '"-algebras and spectral theorem
719
29.1
Operator *-algebras, representations and GNS construction
719
29.2
Spectral theorem, spectral measures, projection valued measures,
functional calculus
723
30
Refined algebraic quantisation (RAQ) and direct integral
decomposition (DID)
729
30.1
RAQ
729
30.2
Master Constraint Programme (MCP) and DID
735
31
Basics of harmonic analysis on compact Lie groups
746
31.1
Representations and
Haar
measures
746
31.2
The Peter and Weyl theorem
752
32
Spin-network functions for SU(2)
755
32.1
Basics of the representation theory of
SU
(2) 755
32.2
Spin-network functions and recoupling theory
757
32.3
Action of holonomy operators on spin-network functions
762
32.4
Examples of coherent state calculations
765
33
+ Functional analytic description of classical connection
dynamics
770
33.1
Infinite-dimensional (symplectic) manifolds
770
References
775
Index
809 |
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| index_date | 2024-07-02T18:44:22Z |
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| institution | BVB |
| isbn | 9780521842631 0521842638 |
| language | English |
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| spelling | Thiemann, Thomas Verfasser aut Modern canonical quantum general relativity Thomas Thiemann 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 XXVI, 819 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge monographs on mathematical physics Quantentheorie General relativity (Physics) Quantum theory Quantentheorie (DE-588)4047992-4 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 s Quantentheorie (DE-588)4047992-4 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016068087&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Thiemann, Thomas Modern canonical quantum general relativity Quantentheorie General relativity (Physics) Quantum theory Quantentheorie (DE-588)4047992-4 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| subject_GND | (DE-588)4047992-4 (DE-588)4112491-1 |
| title | Modern canonical quantum general relativity |
| title_auth | Modern canonical quantum general relativity |
| title_exact_search | Modern canonical quantum general relativity |
| title_exact_search_txtP | Modern canonical quantum general relativity |
| title_full | Modern canonical quantum general relativity Thomas Thiemann |
| title_fullStr | Modern canonical quantum general relativity Thomas Thiemann |
| title_full_unstemmed | Modern canonical quantum general relativity Thomas Thiemann |
| title_short | Modern canonical quantum general relativity |
| title_sort | modern canonical quantum general relativity |
| topic | Quantentheorie General relativity (Physics) Quantum theory Quantentheorie (DE-588)4047992-4 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd |
| topic_facet | Quantentheorie General relativity (Physics) Quantum theory Allgemeine Relativitätstheorie |
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