Details
| Original language | English |
|---|---|
| Article number | 063509 |
| Journal | Journal of mathematical physics |
| Volume | 57 |
| Issue number | 6 |
| Publication status | Published - Jun 2016 |
| Externally published | Yes |
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).
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of mathematical physics, Vol. 57, No. 6, 063509, 06.2016.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations
AU - Stottmeister, A.
AU - Thiemann, T.
PY - 2016/6
Y1 - 2016/6
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=84976381997&partnerID=8YFLogxK
U2 - 10.1063/1.4954228
DO - 10.1063/1.4954228
M3 - Article
VL - 57
JO - Journal of mathematical physics
JF - Journal of mathematical physics
SN - 0022-2488
IS - 6
M1 - 063509
ER -