Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-07-13
Int.J.Mod.Phys. A21 (2006) 5905-5956
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
57 pages; References added, section 2 rewritten and expanded
Scientific paper
10.1142/S0217751X06031661
A theory in which 4-dimensional spacetime is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza-Klein theory. A covariant Dirac equation in curved C-space is explored. The generalized Dirac field is assumed to be a polyvector-valued object (a Clifford number) which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left and/or from the right, and form a large gauge group which may contain the group U(1)xSU(2)xSU(3) of the standard model. The generalized spin connection in C-space has the properties of Yang-Mills gauge fields. It contains the ordinary spin connection related to gravity (with torsion), and extra parts describing additional interactions, including those described by the antisymmetric Kalb-Ramond fields.
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