Coherent states, quantum gravity, and the Born-Oppenheimer approximation. III: Applications to loop quantum gravity (Q2820930)

In this article, the third of three, it is the primary objective to investigate the possibility of formulating a Weyl quantization suitable for loop quantum gravity-type models. Here, an obstacle arises concerning the compatibility of the Weyl quantization with the projective limit structure involved in the construction of the models à la loop quantum gravity. Therefore, the authors analyze how the Weyl quantization for compact Lie groups presented in the second article fits with the projective-phase space structure of these models. For this, in detail they discuss applications of the framework, presented in the previous articles, to models of a loop quantum gravity-type. Their conclusion is that ``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.''NEWLINENEWLINENEWLINEFor Part I and II see [ibid. 57, No. 6, 063509, 21 p. (2016; Zbl 1381.81142); ibid. 57, No. 7, 073501, 77 p. (2016; Zbl 1381.81143)].