Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-01-07
Phys.Rev.D79:064030,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
19 pages, no figures; A reference and footnote added, PACs and minor typos corrected; a significant technical clarification ad
Scientific paper
10.1103/PhysRevD.79.064030
In loop quantum cosmology, Friedmann-LeMaitre-Robertson-Walker (FLRW) space-times arise as well-defined approximations to specific \emph{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 Leibnitz, 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 FLRW models arises as a well-defined reduction of this more fundamental theory.
Ashtekar Abhay
Kaminski Wojciech
Lewandowski Jerzy
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