Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-04-10
JHEP 0704:047,2007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
14 pages, no figures, JHEP format, to appear in JHEP April 2007
Scientific paper
10.1088/1126-6708/2007/04/047
The Arnowitt-Deser-Misner canonical formulation of general relativity is extended to the covariant brane-world theory in arbitrary dimensions. The exclusive probing of the extra dimensions makes a substantial difference, allowing for the construction of a non-constrained canonical theory. The quantum states of the brane-world geometry are defined by the Tomonaga-Schwinger equation, whose integrability conditions are determined by the classical perturbations of submanifolds contained in the Nash's differentiable embedding theorem. In principle, quantum brane-world theory can be tested by current experiments in astrophysics and by near future laboratory experiments at Tev energy. The implications to the black-hole information loss problem, to the accelerating cosmology, and to a quantum mathematical theory of four-sub manifolds are briefly commented.
Fernandes M. C. B.
Maia M. D.
Silva Nildsen
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