Christoffel formula and geodesic motion in hyperspin manifolds

Journal Article · Sat Nov 01 04:00:00 EST 1986 · Int. J. Theor. Phys.; (United States)

DOI:https://doi.org/10.1007/BF00668691· OSTI ID:6924263

Holm, C

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), Journal Name: Int. J. Theor. Phys.; (United States) Vol. 25:11; ISSN IJTPB
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
FIELD THEORIES
GEODESICS
KALUZA-KLEIN THEORY
MAPPING
MATHEMATICAL MANIFOLDS
MATHEMATICAL SPACE
METRICS
MOTION
PARTICLE PROPERTIES
RIEMANN SPACE
SPACE
SPIN
SPINORS
TENSORS
TOPOLOGICAL MAPPING
TRANSFORMATIONS
UNIFIED-FIELD THEORIES