Towards canonical quantum gravity for 3+1 geometries admitting maximally symmetric two-dimensional surfaces

T Christodoulakis (1) , G Doulis (1) , Petros A Terzis (1) , E Melas (2) , Th Grammenos (3) , G O Papadopoulos (4) , A Spanou (5)

1 Department of Physics [Athens]
2 Electrical Engineering Department
3 Department of Mechanical Engineering
4 Department of Mathematics and Statistics
5 School of Applied Mathematics and Physical Sciences

1 Abstract The 3+1 (canonical) decomposition of all geometries admitting two-dimensional space-like surfaces is exhibited. A proposal consisting of a specific re-normalization Assumption and an accompanying Requirement is put forward, which enables the canonical quantization of these geometries, through a generalization of Kuchar's quantization scheme in the case infinite degrees of freedom. The resulting Wheeler-deWitt equation is based on a re-normalized manifold parameterized by three smooth scalar functionals. The entire space of solutions to this equation is analytically given, exploiting the freedom left by the imposition of the Requirement and contained in the third functional.

Mots clés: Physical Sciences

T Christodoulakis, G Doulis, Petros A Terzis, E Melas, Th Grammenos, et al.. Towards canonical quantum gravity for 3+1 geometries admitting maximally symmetric two-dimensional surfaces. Classical and Quantum Gravity, 2010, 27 (14), pp.145018. ⟨10.1088/0264-9381/27/14/145018⟩. ⟨hal-00610058⟩