Neutrino spectrum of Einstein universes

Abstract

The study of higher-dimensional Kaluza–Klein universes constructed from the unitary groups UN is continued. They form Bergmann manifolds of dimension N2 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 UN 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 UN. The neutrino acquires a negligible rest mass of O(10−31 eV) due to the global curvature of our manifold.