2009/01/31 by Abhay Ashtekar, Wojciech Kamiński, Wojciech Kaminski +1 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Hamiltonian constraint #Loop quantum cosmology #Loop quantum gravity #Mathematics #Noncommutative and Quantum Gravity Theories #Open quantum system #Physics #Quantization (signal processing) #Quantum #Quantum algorithm #Quantum cosmology #Quantum dissipation #Quantum dynamics #Quantum field theory #Quantum gravity #Quantum mechanics #Quantum operation #Quantum process #Scalar field #Theoretical physics #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.79.064030
published as Phys.Rev.D79:064030,2009 · 19 pages, no figures; A reference and footnote added, PACs and minor typos corrected; a significant technical clarification added to section IV.A; minor typos corrected; two references added
openalex publication_date 2009/03/27 · arxiv created 2009/06/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In loop quantum cosmology, Friedmann-LeMa\\itre-Robertson-Walker space-times arise as well-defined approximations to specific quantum geometries. We initiate the development of a quantum theory of test scalar fields on these quantum geometries. Emphasis is on the new conceptual ingredients required in the transition from classical space-time backgrounds to quantum space-times. These include a ``relational time'' \`a la Leibniz, the emergence of the Hamiltonian operator of the test field from the quantum constraint equation, and ramifications of the quantum fluctuations of the background geometry on the resulting dynamics. The familiar quantum field theory on classical Friedmann-LeMa\\itre-Robertson-Walker models arises as a well-defined reduction of this more fundamental theory.