Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-01-15
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
34 pages
Scientific paper
Some mathematical aspects of using the translation group as an internal symmetry group in a gauge field theory are presented and discussed. The traditional manner in which gravitation can be accounted for by the introduction of a global frame field on a parallelizable spacetime is reviewed. It is then discussed in the more general context of a global frame field on the bundle of linear frames. In the process, the elements of variational field theory for physical fields defined on G-structures are set down. It is suggested that it is probably more proper to attribute gravitation to a reduction of the bundle of linear frames to {e} -- at least over a generic submanifold of spacetime -- than to a reduction to the Lorentz group since the Lorentz group is more intrinsic to electromagnetism and gravitation has the character of a "residual" symmetry of spacetime at the astrophysical level.
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