Neutrino spectrum of Einstein universes
The study of higher-dimensional Kaluza--Klein universes constructed from the unitary groups U/sub N/ is continued. They form Bergmann manifolds of dimension N/sup 2/ with Finslerian geometry induced by their hyperspin structure. In this paper Lagrangians for relativistic wave equations, which are generalizations of the Klein--Gordan, Dirac, and Weyl neutrino equations, are formulated. The wave equations are in general of differential order N. The hyperneutrino equation is examined in detail as the simplest example and its discrete symmetries are discussed. It is found that for N = 3 and N>4 TCP and all its constituent symmetries are violated. The boson calculus is used to solve the linear neutrino equation exactly on U/sub N/ and the energy spectra of the neutrino and antineutrino are presented. It is found that the density ratio of negative to positive energy states is unity only for N = 2, producing asymmetry for all higher-dimensional U/sub N/. The neutrino acquires a negligible rest mass of O(10/sup -31/ eV) due to the global curvature of our manifold.
- Research Organization:
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30322
- OSTI ID:
- 6790281
- Journal Information:
- J. Math. Phys. (N.Y.); (United States), Vol. 29:10, Issue 10
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
COSMOLOGICAL MODELS
GENERAL RELATIVITY THEORY
GRAVITATION
KALUZA-KLEIN THEORY
EINSTEIN FIELD EQUATIONS
MATHEMATICAL MANIFOLDS
NEUTRINOS
REST MASS
U GROUPS
UNIFIED-FIELD THEORIES
WAVE EQUATIONS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
FIELD EQUATIONS
FIELD THEORIES
LEPTONS
LIE GROUPS
MASS
MASSLESS PARTICLES
MATHEMATICAL MODELS
PARTIAL DIFFERENTIAL EQUATIONS
SYMMETRY GROUPS
657003* - Theoretical & Mathematical Physics- Relativity & Gravitation