The hyperspin structure of Einstein universes and their neutrino spectrum

Miscellaneous · Thu Jan 01 00:00:00 EST 1987

OSTI ID:5116641

Holm, C L

This thesis formulates and studies a sequence of homogeneous, isotropic, and compact solutions to the empty space hypergravity equations (Finkelstein 1987). These solutions are hyperspin manifolds constructed from unitary groups U{sub N}:= U(N,C) and describe the static compact N{sup 2} dimensional Einstein universes of the Kaluza-Klein type with Finslerian geometry. By taking the universal covering group of U{sub N} we obtain a manifold with topology IRxSU{sub N}, where the abelian group IR is the time axis and SU{sub N} provides a compact homogeneous spatial part. To describe the geometry of these manifolds we extend the exterior Cartan-Penrose calculus from spinors to hyperspinors and apply the Maurer-Cartan equations to obtain the hyperspin structure of U{sub N}. We present a natural extension to curved time space of the relativistic wave equations which are in general of differential order N and discuss the discrete symmetries of the hyperneutrino equation. We solve the linear neutrino equation exactly and present the energy spectra of the neutrino and antineutrino, which differ for N > 2. The neutrino acquires a negligible rest mass of O(10{sup {minus}31}eV). Our most important conclusion is that there is a consistent alternative to the usual Riemannian geometry for spaces with internal dimensions, which deserves further study.

• Research Organization: Georgia Inst. of Tech., Atlanta, GA (USA)
• OSTI ID: 5116641
• Resource Relation: Other Information: Thesis (Ph. D.)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
GRAVITATIONAL FIELDS
MATHEMATICAL MODELS
CALCULATION METHODS
FIELD THEORIES
KALUZA-KLEIN THEORY
MATHEMATICAL MANIFOLDS
WAVE EQUATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
UNIFIED-FIELD THEORIES
657003* - Theoretical & Mathematical Physics- Relativity & Gravitation