Hanusch, Maximilian: Invariant connections and symmetry reduction in loop quantum gravity. 2014
Content
- Introduction
- Quantum Gravity
- Mathematical Context
- Invariant and Generalized Connections
- Symmetry Reduction
- Projective Structures and Normalized Radon Measures
- Aims and Organization
- Preliminaries
- Special Mathematical Background
- Spectral Extensions of Group Actions
- Group Actions on Spectra
- Invariant and Generalized Connections
- Homomorphisms of Paths and Invariance
- Summary
- Modification of Invariant Homomorphisms
- Analytic and Lie Algebra Generated Curves
- Modifications along Lie Algebra Generated Curves
- Inclusion Relations
- Modifications along Free Segments
- Summary
- Measures on Quantum-Reduced Configuration Spaces
- Homogeneous Isotropic LQC
- Setting
- Group Structures, Actions and some Measure Theoretical Aspects
- Quantization vs. Reduction
- Motivation of the Construction
- Projective Structures on R
- Radon Measures on R
- Summary
- A Characterization of Invariant Connections
- Conclusions and Outlook
- Appendix to Preliminaries
- Appendix to Special Mathematical Background
- Appendix to Spectral Extensions of Group Actions
- Appendix to Modification of Invariant Homomorphisms
- Appendix to Lie Algebra Generated Configuration Spaces
- Appendix to Homogeneous Isotropic LQC
- Appendix to A Characterization of Invariant Connections
- The Proof of the Case in Subsection 8.3.3
- A Result used in the End of Section 8.3
- Spherically Symmetric Connections
- Symbols