Quantum Mechanical Formulation Of Quantum Cosmology For Brane-World Effective Action

Details Quantum Mechanical Formulation Of Quantum Cosmology For Brane-World Effective Action Quantum Mechanical Formulation Of Quantum Cosmology For Brane-World Effective Action

2003-05-12

arxiv.org/abs/gr-qc/0305042v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages, Latex

Scientific paper

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.

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