Gravitation and the Local Symmetry Group of Spacetime

Details Gravitation and the Local Symmetry Group of Spacetime Gravitation and the Local Symmetry Group of Spacetime

2002-01-17

arxiv.org/abs/gr-qc/0201059v2

Int.J.Theor.Phys. 41 (2002) 729-736

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, no figures. Some signs and references corrected; version to appear in Int. J. Theor. Phys

Scientific paper

According to general relativity, the interaction of a matter field with gravitation requires the simultaneous introduction of a tetrad field, which is a field related to translations, and a spin connection, which is a field assuming values in the Lie algebra of the Lorentz group. These two fields, however, are not independent. By analyzing the constraint between them, it is concluded that the relevant local symmetry group behind general relativity is provided by the Lorentz group. Furthermore, it is shown that the minimal coupling prescription obtained from the Lorentz covariant derivative coincides exactly with the usual coupling prescription of general relativity. Instead of the tetrad, therefore, the spin connection is to be considered as the fundamental field representing gravitation.

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