2003/05/12 by Abhik Kumar Sanyal, Sanyal, Abhik Kumar · 1 citation
Physics and Astronomy · #Cosmology and Gravitation Theories #Relativity and Gravitational Theory #Solar and Space Plasma Dynamics #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0305042
6 pages, Latex
arxiv created 2003/05/12 · arxiv updated 2009/11/30
Canonical quantization of the Brane-World effective action presented by Kanno and Soda containing higher order curvature invariant terms, has been performed. It requires introduction of an auxiliary variable. As observed in a series of publications by Sanyal and Modak, here again we infer that properly chosen auxiliary variable leads to a Schrodinger like equation where the kinetic part of a canonical variable disentangles from the rest of the variables giving a natural quantum mechanical flavour of time. Further, the effective Hamiltonian turns out to be hermitian, leading to the continuity ewuation. Thus, a quantum mechanical probability inter pretation is plausible. Finally, the extremization of the effective potential leads to Einstein's equation and a well behaved classical solution, which is a desirable feature of the gravitational action containing higher order curvature invariant terms.