Quantum field theory on a cosmological, quantum space-time
Abstract
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.
Cite
@article{arxiv.0901.0933,
title = {Quantum field theory on a cosmological, quantum space-time},
author = {Abhay Ashtekar and Wojciech Kaminski and Jerzy Lewandowski},
journal= {arXiv preprint arXiv:0901.0933},
year = {2009}
}
Comments
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