Canonical quantization of static spherically symmetric geometries

NEB 15 – Recent Developments in Gravity

Christodoulakis, T.^1 ; Dimakis, N.^1 ; Terzis, P.A.^1 ; Doulis, G.^2 ; Grammenos, Th.^3 ; Melas, E.^4 ; Spanou, A.^5

Nuclear and Particle Physics Section, Physics Department, University of Athens, GR 157-71 Athens, Greece^1

Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9010, New Zealand^2

Department of Civil Engineering, University of Thessaly, GR 383-34 Volos, Greece^3

Logistics Department, Technological Educational Institution of Chalkida, GR 32-200, Thiva, Greece^4

School of Applied Mathematics and Physical Sciences, National Technical University of Athens, GR 157-80, Athens, Greece^5

关键词: Canonical quantization;    Casimir invariants;    Dynamical evolution;    Einstein-Hilbert action;    Integrability;    Parametrizations;    Reparametrization;    Symmetric geometry;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/453/1/012002/pdf
DOI  :  10.1088/1742-6596/453/1/012002

来源: IOP

【 摘 要 】

The conditional symmetries of the reduced Einstein-Hilbert action emerging from a static, spherically symmetric geometry are used as supplementary conditions on the wave function. Based on their integrability conditions, only one of the three existing symmetries can be consistently imposed, while the unique Casimir invariant, being the product of the remaining two symmetries, is calculated as the only possible second condition on the wave function. This quadratic integral of motion is identified with the reparametrization generator, as an implication of the uniqueness of the dynamical evolution, by fixing a suitable parametrization of the r-lapse function. In this parametrization, the determinant of the supermetric plays the role of the mesure. The combined Wheeler-DeWitt and linear conditional symmetry equations are analytically solved. The solutions obtained depend on the product of the two "scale factors".