Brane-world Quantum Gravity

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 quantu...

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Bibliographic Details
Published in:arXiv.org 2007-04
Main Authors: Maia, M D, Silva, Nildsen, Fernandes, M C B
Format: Article
Language:English
Subjects:
Astrophysics
Cosmology
Integral calculus
Integral equations
Manifolds (mathematics)
Quantum gravity
Relativity
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0704.1289