Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-01-09
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
4 pages, title changed, minor grammar corrections
Scientific paper
An origin and necessity of so called conformal (or,Penrose-Chernikov-Tagirov) coupling of scalar field to the metric of n-dimensional Riemannian space-time is discussed in brief. The corresponding general-relativistic field equation implies a one-particle (quantum mechanical) Schrodinger Hamiltonian which depends on the space-time dimensionality n, contrary to the Hamiltonian constructed by quantization of geodesic motion, which is the same for any value of n. In general, the Hamiltonians can coincide only for n = 4, the dimensionality of the ordinarily observed Universe. In view of the fundamental role of a scalar field in various cosmological models, this fact may be of interest for models of brane worlds where n > 4 .
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