TITLE:
Fundamental Fields as Eigenvectors of the Metric Tensor in a 16-Dimensional Space-Time
AUTHORS:
Alberto Strumia
KEYWORDS:
Field Theory, Field Unification, General Relativity, Standard Model, Elementary Particles
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.6,
June
30,
2019
ABSTRACT: An alternative approach to the usual Kaluza-Klein
way to field unification is presented which seems conceptually more
satisfactory and elegant. The main idea is that of associating each fundamental
interaction and matter field with a vector potential which is an eigenvector of
the metric tensor of a multidimensional space-time manifold (n-dimensional “vierbein”). We deduce a system
of field equations involving both Einstein and Maxwell-like equations for the
fundamental fields. Confinement of the fields within the observable 4-dimensional space-time and
non-vanishing particles’ rest mass problem are shown to be related to the choice of a
scalar boson field (Higgs boson) appearing in the theory as a gauge function. Physical interpretation of the results, in order that all the known
fundamental interactions may be included within the metric and connection,
requires that the extended space-time is 16-dimensional. Fermions are shown to be included within the
additional components of the vector potentials arising because of the increased
dimensionality of space-time. A cosmological solution is also presented
providing a possible explanation both to space-time flatness and to dark matter
and dark energy as arising from the field components hidden within the extra
space dimensions. Suggestions for gravity quantization are also examined.