A mystery of conformal coupling

E. A. Tagirov

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arXiv · gr-qc/0501026

A mystery of conformal coupling

E. A. Tagirov

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Abstract

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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E. A. Tagirov. 2005-01-28. A mystery of conformal coupling. https://arxiv.org/abs/gr-qc/0501026

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