2006/12/21 by Tim Koslowski, Koslowski, Tim · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0612138
48 pages, no figures, LaTeX
arxiv created 2006/12/21 · openalex publication_date 2006/12/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper serves as a preparation of work that focuses on extracting cosmological sectors from Loop Quantum Gravity. We start with studying the extraction of subsystems from classical systems. A classical Hamiltonian system can be reduced to a subsystem of ''relevant observables'' using the pull-back under the Poisson-embedding of the ''relevant part of phase space'' into full phase space. Since a quantum theory can be thought of as a noncommutative phase space, one encounters the problem of embedding noncommutative spaces. We solve this problem for a physically interesting set of quantum systems and embeddings by constructing the noncommutative analogue of the construction of an embedding as the projection to the base space of an embedding of fibre bundles over the involved spaces. This paper focuses on the physical ideas that enter our programme of reduction of quantum theories and tries to explain these on examples rather than abstractly, which will be the focus of a forthcoming paper.