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marcus

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## Main Question or Discussion Point

Atyy spotted 3 potentially important LQG papers and added them to the biblio thread. The B-O approximation has proven essential in quantum chemistry and similar applications dealing with wave functions of complex systems with many components. Geometry is such a system and it seems reasonable that B-O, applied to QG, could play a key role in LQG.

I'll list the three papers, and then give some overview and introduction to the Born-Oppenheimer approximation, excerpting and referencing the Wikipedia article.

==excerpts==

http://arxiv.org/abs/1504.02169

Alexander Stottmeister, Thomas Thiemann

(Submitted on 9 Apr 2015)

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. ...

http://arxiv.org/abs/1504.02170

Alexander Stottmeister, Thomas Thiemann

(Submitted on 9 Apr 2015)

In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. ...

http://arxiv.org/abs/1504.02171

Alexander Stottmeister, Thomas Thiemann

(Submitted on 9 Apr 2015)

In this article, the third of three, we analyse how the Weyl quantisation for compact Lie groups presented in the second article of this series fits with the projective-phase space structure of loop quantum gravity-type models. Thus, the proposed Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity.

==endquote==

I'll list the three papers, and then give some overview and introduction to the Born-Oppenheimer approximation, excerpting and referencing the Wikipedia article.

==excerpts==

http://arxiv.org/abs/1504.02169

**Coherent states, quantum gravity and the Born-Oppenheimer approximation, I: General considerations**Alexander Stottmeister, Thomas Thiemann

(Submitted on 9 Apr 2015)

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. ...

http://arxiv.org/abs/1504.02170

**Coherent states, quantum gravity and the Born-Oppenheimer approximation, II: Compact Lie Groups**Alexander Stottmeister, Thomas Thiemann

(Submitted on 9 Apr 2015)

In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. ...

http://arxiv.org/abs/1504.02171

**Coherent states, quantum gravity and the Born-Oppenheimer approximation, III: Applications to loop quantum gravity**Alexander Stottmeister, Thomas Thiemann

(Submitted on 9 Apr 2015)

In this article, the third of three, we analyse how the Weyl quantisation for compact Lie groups presented in the second article of this series fits with the projective-phase space structure of loop quantum gravity-type models. Thus, the proposed Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity.

==endquote==