Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1997-10-03
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
12 pages, LaTeX, no figures, Summary of talk given in the Analysis of Dirac Operators section at the meeting of the Internatio
Scientific paper
A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted to represent internal structure of matter (e.g. classical or quantum spin). The generalized Dirac operator must now include differentiation with respect to these higher order geometric coordinates. In a Riemann space, where the magnitude and rank of geometric objects are preserved under displacement, these new terms modify the geodesics. One possible physical interpretation is natural coupling of the classical spin to linear motion, providing a new derivation of the Papapetrou equations. A generalized curvature is proposed for the Clifford manifold in which the connection does not preserve the rank of a multivector under parallel transport, e.g. a vector may be ``rotated'' into a scalar.
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