Journal article


Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations


Publication Details
Author(s): Stottmeister A, Thiemann T
Publisher: AMER INST PHYSICS
Publication year: 2016
Volume: 57
Journal issue: 6
ISSN: 0022-2488

Abstract

This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields). Published by AIP Publishing.



How to cite
APA: Stottmeister, A., & Thiemann, T. (2016). Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations. Journal of Mathematical Physics, 57(6). https://dx.doi.org/10.1063/1.4954228

MLA: Stottmeister, Alexander, and Thomas Thiemann. "Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations." Journal of Mathematical Physics 57.6 (2016).

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