Modern Canonical Quantum General Relativity

Produktbeschreibung

Canonical quantisation and loop quantum gravity theory for graduate students of quantum field theory. 

Inhaltsverzeichnis

Preface; Notation and conventions; Introduction; Part I. Classical Foundations,
Interpretation and the Canonical Quantisation Programme: 1. Classical
Hamiltonian formulation of general relativity; 2. The problem of time, locality
and the interpretation of quantum mechanics; 3. The programme of canonical
quantisation; 4. The new canonical variables of Ashtekar for general relativity;
Part II. Foundations of Modern Canonical Quantum General Relativity: 5.
Introduction; 6. Step I: the holonomy-flux algebra [P]; 7. Step II:
quantum-algebra; 8. Step III: representation theory of [A]; 9. Step IV: 1.
Implementation and solution of the kinematical constraints; 10. Step V: 2.
Implementation and solution of the Hamiltonian constraint; 11. Step VI:
semiclassical analysis; Part III. Physical Applications: 12. Extension to
standard matter; 13. Kinematical geometrical operators; 14. Spin foam models;
15. Quantum black hole physics; 16. Applications to particle physics and quantum
cosmology; 17. Loop quantum gravity phenomenology; Part IV. Mathematical Tools
and their Connection to Physics: 18. Tools from general topology; 19.
Differential, Riemannian, symplectic and complex geometry; 20. Semianalytical
category; 21. Elements of fibre bundle theory; 22. Holonomies on non-trivial
fibre bundles; 23. Geometric quantisation; 24. The Dirac algorithm for field
theories with constraints; 25. Tools from measure theory; 26. Elementary
introduction to Gel'fand theory for Abelean C* algebras; 27. Bohr
compactification of the real line; 28. Operatir -algebras and spectral theorem;
29. Refined algebraic quantisation (RAQ) and direct integral decomposition
(DID); 30. Basics of harmonic analysis on compact Lie groups; 31. Spin network
functions for SU(2); 32. + Functional analytical description of classical
connection dynamics; Bibliography; Index. 

Autoreninfo

Thomas Thiemann is Staff Scientist at the Max Planck Institut für Gravitationsphysik (Albert Einstein Institut), Potsdam, Germany. He is also a long-term researcher at the Perimeter Institute for Theoretical Physics and Associate Professor at the University of Waterloo, Canada. Thomas Thiemann obtained his PhD in theoretical physics from the Rheinisch-Westfälisch Technische Hochschule, Aachen, Germany. He held two year postdoctoral positions at The Pennsylvania State University and Harvard University. As of 2005 he holds a guest professor position at Beijing Normal University, China.