2005/01/09 by E. A. Tagirov, Tagirov, E. A.
Chemistry · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Molecular spectroscopy and chirality #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.gr-qc/0501026
4 pages, title changed, minor grammar corrections
openalex publication_date 2005/01/09 · arxiv created 2005/01/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 .