Towards the QFT on curved spacetime limit of QGR: II. A concrete implementation
Abstract
The present paper is the companion of Sahlmann and Thiemann (2006 Towards the QFT on curved spacetime limit of QGR: I. A general scheme Class. Quantum Grav. 23 867) in which we proposed a scheme that tries to derive the quantum field theory (QFT) on curved spacetimes (CST) limit from backgroundindependent quantum general relativity (QGR). The constructions of the companion paper make heavy use of the notion of semiclassical states for QGR. In the present paper, we employ the complexifier coherent states for QGR recently proposed by Thiemann and Winkler as semiclassical states, and thus fill the general formulae obtained in the companion paper with life. We demonstrate how one can, under some simplifying assumptions, explicitly compute expectation values of the operators relevant for the gravity matter Hamiltonians of the companion paper in the complexifier coherent states. These expectation values give rise to effective matter Hamiltonians on the background on which the gravitational coherent state is peaked and thus induce approximate notions of nparticle states and matter propagation on fluctuating spacetimes. We display the details for the scalar and the electromagnetic field. The effective theories exhibit two types of corrections as compared to the ordinary QFT on CST. The first is due to the quantum fluctuations of the gravitational field and the second arises from the fact that background independence forces both geometry and matter to propagate on a spacetime of the form {\bb R}\times\gamma , where γ is a (random) graph. Finally, we obtain explicit numerical predictions for nonstandard dispersion relations for the scalar and the electromagnetic field. They should, however, not be taken too seriously, due to the many ambiguities in our scheme, the analysis of the physical significance of which has only begun. We show, however, that one can classify these ambiguities at least in broad terms.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 February 2006
 DOI:
 10.1088/02649381/23/3/020
 arXiv:
 arXiv:grqc/0207031
 Bibcode:
 2006CQGra..23..909S
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 LaTeX, 49 p., one figure