Towards the QFT on curved spacetime limit of QGR: I. A general scheme
Journal article
(Original article)
Publication Details
Author(s): Sahlmann H, Thiemann T
Journal: → Classical and Quantum Gravity 
Publisher: Institute of Physics: Hybrid Open Access
Publication year: 2006
Volume: 23
Journal issue: 3
Pages range: 867908
ISSN: 02649381
Abstract
In this paper and the companion paper (Sahlmann and Thiemann 2006 Towards the QFT on curved spacetime limit of QGR: II. A concrete implementation Class. Quantum Grav. 23 909), we address the question of how one might obtain the semiclassical limit of ordinary matter quantum fields (QFT) propagating on curved spacetimes (CST) from fullfledged quantum general relativity (QGR), starting from first principles. We stress that we do not claim to have a satisfactory answer to this question, rather our intention is to ignite a discussion by displaying the problems that have to be solved when carrying out such a programme. In the first paper of this series of two, we propose a general scheme of logical steps that one has to take in order to arrive at such a limit. We discuss the technical and conceptual problems that arise in doing so and how they can be solved in principle. As to be expected, completely new issues arise due to the fact that QGR is a backgroundindependent theory. For instance, fundamentally the notion of a photon involves not only the Maxwell quantum field but also the metric operator  in a sense, there is no photon vacuum state but a 'photon vacuum operator'! Such problems have, to the best of our knowledge, not been discussed in the literature before, we are facing squarely one aspect of the deep conceptual difference between a backgrounddependent and a backgroundfree theory. While in this first paper we focus on conceptual and abstract aspects, for instance the definition of (fundamental) nparticle states (e.g. photons), in the second paper we perform detailed calculations including, among other things, coherent state expectation values and propagation on random lattices. These calculations serve as an illustration of how far one can get with present mathematical techniques. Although they result in detailed predictions for the size of first quantum corrections such as the γray burst effect, these predictions should not be taken too seriously because (a) the calculations are carried out at the kinematical level only and (b) while we can classify the amount of freedom in our constructions, the analysis of the physical significance of possible choices has just begun. © 2006 IOP Publishing Ltd.
FAU Authors / FAU Editors
 Sahlmann, Hanno Prof. Dr. 
  Professur für Theoretische Physik 

 Thiemann, Thomas Prof. Dr. 
  Chair for Theoretical Physics III (Quantum Gravity) 

How to cite
APA:  Sahlmann, H., & Thiemann, T. (2006). Towards the QFT on curved spacetime limit of QGR: I. A general scheme. Classical and Quantum Gravity, 23(3), 867908. https://dx.doi.org/10.1088/02649381/23/3/019 
MLA:  Sahlmann, Hanno, and Thomas Thiemann. "Towards the QFT on curved spacetime limit of QGR: I. A general scheme." Classical and Quantum Gravity 23.3 (2006): 867908. 