Brane-world Quantum Gravity

Abstract

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.

14 pages, no figures, JHEP format, to appear in JHEP April 2007

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Cited by in corpus (6)

• Classical tests in brane gravity
• Geometrical aspects on the dark matter problem
• On the thermal stability of a static spherically symmetric black holes in Nash embedding framework
• Lower tensor-to-scalar ratio as possible signature of modified gravity
• Variation of mass in primordial nucleosynthesis as a test of Induced Matter Brane Gravity
• Probing dynamical embeddings in a five-dimensional spacetime in light of DESI BAO