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Title: The hyperspin structure of Einstein universes and their neutrino spectrum

Abstract

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,more » which deserves further study.« less

Authors:
Publication Date:
Research Org.:
Georgia Inst. of Tech., Atlanta, GA (USA)
OSTI Identifier:
5116641
Resource Type:
Miscellaneous
Resource Relation:
Other Information: Thesis (Ph. D.)
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Holm, C L. The hyperspin structure of Einstein universes and their neutrino spectrum. United States: N. p., 1987. Web.
Holm, C L. The hyperspin structure of Einstein universes and their neutrino spectrum. United States.
Holm, C L. 1987. "The hyperspin structure of Einstein universes and their neutrino spectrum". United States.
@article{osti_5116641,
title = {The hyperspin structure of Einstein universes and their neutrino spectrum},
author = {Holm, C L},
abstractNote = {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.},
doi = {},
url = {https://www.osti.gov/biblio/5116641}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Jan 01 00:00:00 EST 1987},
month = {Thu Jan 01 00:00:00 EST 1987}
}

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