de
en
Schliessen
Detailsuche
Bibliotheken
Projekt
Impressum
Datenschutz
Schliessen
Publizieren
Besondere Sammlungen
Digitalisierungsservice
Hilfe
Impressum
Datenschutz
zum Inhalt
Detailsuche
Schnellsuche:
OK
Ergebnisliste
Titel
Titel
Inhalt
Inhalt
Seite
Seite
Im Werk suchen
Kaminski, Diana: Some operator algebraic techniques in Loop Quantum Gravity. 2011
Inhalt
Overview
Contents
Preface
I Quantisation of gravity in the Loop Quantum Gravity approach
An overview about General Quantum Physics and Quantum Gravity
The Ashtekar formulation of Classical Gravity
Quantisation procedures of a classical system
Some algebras in Physics
Algebras in Quantum Mechanics
Algebras in Quantum Field Theory
Algebras for Lattice Gauge Theories and Statistical Mechanics
General mathematical concepts for the construction of C*-algebras
Pontryagin duality, quantum groups and cross-product algebras
O*- and C*-algebras generated by unbounded and bounded operators
A short summary about algebras in Loop Quantum Gravity and Cosmology
Algebras in Loop Quantum Cosmology
Algebras in Loop Quantum Gravity
Comparison of QM, QFT and LQG algebras
Quantum constraints, KMS-Theory and dynamics
The implementation of quantum constraints on algebras of Loop Quantum Gravity
The classical hypersurface deformation constraint algebra
The quantum spatial diffeomorphism constraints
The quantum Hamilton constraint
The classical Thiemann Master constraint, Dirac and complete observables
KMS-Theory in Generally Covariant Theories
A summary of physical algebras of quantum operators in LQG
The configuration and momentum space of loop quantum gravity
Path, gauge and Lie groupoids
Loop spaces, loop and holonomy group
Fundamental groupoids of path spaces
Finite path groupoids and graph systems
General Lie and gauge groupoids
Transformations in a Lie groupoid
Duality of connections and holonomies
Infinitesimal geometric objects for a gauge theory
Integrated infinitesimals, path connections, holonomy groupoids and holonomy maps in groupoids
Holonomy maps and transformations in groupoids and graph systems
Holonomy maps for Yang Mills theories
Holonomy maps for gravitational theories
Holonomy maps and transformations for a gauge theory
Holonomy maps for finite path groupoids, graph systems and transformations
Holonomy maps for path groupoids
Classical and quantum flux variables
The classical flux variables
The Lie algebra-valued quantum flux operators associated to surfaces and graphs
The group-valued quantum flux operators associated to surfaces and graphs
The group-valued quantum flux operators associated to surfaces and finite path groupoids
II Quantum algebras of Loop Quantum Gravity and Cosmology
The quantum algebras of Loop Quantum Cosmology
The algebra of almost periodic functions
Weyl algebras over pre-symplectic spaces and Weyl algebra of LQC
The smooth holonomy C*-algebra
The algebra of almost periodic functions on the loop group
The cylindrical function C*-algebra for path groupoids
The modified Wilson C*-algebra
The analytic holonomy C*-algebra and Weyl C*-algebra
Dynamical systems of actions of the flux group on the analytic holonomy C*-algebra
Dynamical systems of actions of the group of bisections on two C*-algebras
Weyl C*-algebras associated to surfaces and inductive limits of finite graph systems
Flux and graph-diffeomorphism group-invariant states of the Weyl C*-algebra for surfaces
The holonomy-flux von Neumann algebra and the Weyl C*-algebra for surfaces
The holonomy-flux cross-product C*-algebra
The flux and flux transformation group, n.c. and heat-kernel-holonomy C*-algebra
The holonomy-flux cross-product C*-algebra for surface sets
The holonomy-flux cross-product C*-algebra for a finite graph system and a surface set
The holonomy-flux cross-product C*-algebra for surfaces
The holonomy-flux-graph-diffeomorphism cross-product C*-algebra
The group and the transformation group C*-algebra in Loop Quantum Cosmology
Analytic holonomy and holonomy-flux cross-product *-algebras
Some analytic holonomy *-algebras
The holonomy-flux cross-product *-algebra
The construction of the holonomy-flux cross-product *-algebra
Heisenberg holonomy-flux cross-product *-algebras
Representations and states of the holonomy-flux cross-product *-algebra
Tensor products of the holonomy-flux cross-product *-algebra
The localised holonomy-flux cross-product *-algebra
The localised holonomy *-algebra
A representation of the general localised part of the localised holonomy-flux cross-product *-algebra
C*-dynamical systems, KMS-states and the localised holonomy-flux cross-product *-algebra
The modified quantum Hamilton constraint operator
The holonomy-flux Nelson transform C*-algebra
Holonomy groupoid and holonomy-flux groupoid C*-algebras for gauge theories
The construction of the holonomy groupoid C*-algebra for gauge theories
Cross-product C*-algebras for gauge theories
Covariant holonomy groupoid formulation of LQG
Conclusion and Outlook
III Comparison tables, Appendix, Symbols, Index and References
Comparison tables
Appendix
Some mathematical objects in Differential Geometry
Infinitesimal connections on principal bundles
Some mathematical objects in Operator Algebra Theory
Topological spaces and groups
Hopf *-algebras
Operator Theory in the O*-algebra framework
Operator Theory in the C*-algebra framework
Banach *-algebras
Symbols
Index
References
Die detaillierte Suchanfrage erfordert aktiviertes Javascript.