Christoffel formula and geodesic motion in hyperspin manifolds
A hyperspin manifold S/sub N/ constructed from N-component hyperspinors is an alternative to Riemannian manifolds R/sup n/ for Kaluza-Klein-type theories of higher dimensions. Hyperspin manifolds posses a fundamental chronometric tensor with N n-valued indices, where always n = N/sup 2/. Some concepts of Riemannian geometry therefore have to be extended. A hyper-Christoffel formula is presented that expresses the connection in terms of the chronometric, assuming the chronometric is covariantly constant and the connection is torsion-free. Thus, the chronometric can be used as sole dynamical variable. Extremals and selfparallel curves, which coincide in Riemannian manifolds, in general differ in hyperspin manifolds, but coincide again for nonnull curves.
- Research Organization:
- Georgia Institute of Technology, Atlanta, GA
- OSTI ID:
- 6924263
- Journal Information:
- Int. J. Theor. Phys.; (United States), Vol. 25:11
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
KALUZA-KLEIN THEORY
MATHEMATICAL MANIFOLDS
SPIN
GEODESICS
METRICS
MOTION
RIEMANN SPACE
SPINORS
TENSORS
TOPOLOGICAL MAPPING
ANGULAR MOMENTUM
FIELD THEORIES
MAPPING
MATHEMATICAL SPACE
PARTICLE PROPERTIES
SPACE
TRANSFORMATIONS
UNIFIED-FIELD THEORIES
645400* - High Energy Physics- Field Theory