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Symmetry 2018, 10(3), 70; doi:10.3390/sym10030070

Symmetries in Classical and Quantum Treatment of Einstein’s Cosmological Equations and Mini-Superspace Actions

1
Nuclear and Particle Physics Section, Physics Department, University of Athens, GR 157-71 Athen, Greece
2
Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00 Prague 8, Czech Republic
*
Author to whom correspondence should be addressed.
Received: 17 February 2018 / Revised: 12 March 2018 / Accepted: 13 March 2018 / Published: 16 March 2018
(This article belongs to the Special Issue Symmetry in Cosmology)
View Full-Text   |   Download PDF [273 KB, uploaded 16 March 2018]

Abstract

The use of automorphisms of the various Bianchi-type Lie algebras as Lie-point symmetries of the corresponding Einstein field equations entails a reduction of their order and ultimately leads to the entire solution space. When a valid reduced action principle exists, the symmetries of the configuration mini-supermetric space can also be used, in conjunction with the constraints, to provide local or non-local constants of motion. At the classical level, depending on their number, these integrals can even secure the acquisition of the entire solution space without any further solving of the dynamical equations. At the quantum level, their operator analogues can be used, along with the Wheeler–DeWitt equation, to define unique wave functions that exhibit singularity-free behavior at a semi-classical level. View Full-Text
Keywords: Symmetries of ODE’s; Einstein cosmological actions; minisuperspace Symmetries of ODE’s; Einstein cosmological actions; minisuperspace
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Christodoulakis, T.; Karagiorgos, A.; Zampeli, A. Symmetries in Classical and Quantum Treatment of Einstein’s Cosmological Equations and Mini-Superspace Actions. Symmetry 2018, 10, 70.

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