Hyperspin manifolds

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

DOI:https://doi.org/10.1007/BF00670769· OSTI ID:6939888

Finkelstein, D; Finkelstein, S R; Holm, C

Riemannian manifolds are but one of three ways to extrapolate from fourdimensional Minkowskian manifolds to spaces of higher dimension, and not the most plausible. If we take seriously a certain construction of time space from spinors, and replace the underlying binary spinors by N-ary hyperspinors with new ''internal'' components besides the usual two ''external'' ones, this leads to a second line, the hyperspin manifolds /sub n/ and their tangent spaces d/sub n/, different in structure and symmetry group from the Riemannian line, except that the binary spaces d /sub 2/ (Minkowski time space) and /sub 2/ (Minkowskian manifold) lie on both. d/sub n/ and /sub n/ have dimension n = N/sup 2/. In hyperspin manifolds the energies of modes of motion multiply instead of adding their squares, and the N-ary chronometric form is not quadratic, but N-ic, with determinantal normal form. For the nine-dimensional ternary hyperspin manifold, we construct the trino, trine-Gordon, and trirac equations and their mass spectra in flat time space. It is possible that our four-dimensional time space sits in a hyperspin manifold rather than in a Kaluza-Klein Riemannian manifold. If so, then gauge quanta with spin-3 exist.

• Research Organization: Georgia Institute of Technology, Atlanta, GA
• OSTI ID: 6939888
• Journal Information: Int. J. Theor. Phys.; (United States), Journal Name: Int. J. Theor. Phys.; (United States) Vol. 25:4; 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
FOUR-DIMENSIONAL CALCULATIONS
INVARIANT IMBEDDING
MASS SPECTRA
MATHEMATICAL MANIFOLDS
MATHEMATICAL SPACE
MINKOWSKI SPACE
PARTICLE PROPERTIES
QUANTUM FIELD THEORY
RIEMANN SPACE
SPACE
SPACE-TIME
SPECTRA
SPIN
SPINOR FIELDS
SPINORS