2018/11/22 by Jia-An Lu, Lu, Jia-An
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Cosmology and Gravitation Theories
paper · pdf · doi:10.48550/arxiv.1811.09159
The Hamiltonian formalism of Einstein--Cartan (EC) gravity is a starting point for canonical quantum gravity. The existing formalisms are at most Lorentz covariant, or diffeomorphism covariant. Here we analyze the Hamiltonian EC gravity in a 5d covariant way, with the gauge group being the de Sitter (dS) group, which unifies the Lorentz transformations and translation in an elegant manner, and also coincides with the acceleration of the universe. We reformulate the EC equations into a dS-covariant form, then find out the dS-covariant constraints of the phase space, and make all the constraint functions constitute a closed algebra by constructing a dS-invariant Dirac bracket, for the purpose of quantization.