Author(s)

Alberto Strumia^1,2,3

¹Mathematical Physics, C.I.R.A.M., University of Bologna, Bologna, Italy.
²Department of Mathematics Mathematics, University of Bari, Bari, Italy.
³Istituto Nazionale di Alta Matematica\F. Severi (i.n.d.a.m.), Rome, Italy.

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.

Field Theory, Field Unification, General Relativity, Standard Model, Elementary Particles

Strumia, A. (2019) Fundamental Fields as Eigenvectors of the Metric Tensor in a 16-Dimensional Space-Time. Journal of Applied Mathematics and Physics, 7, 1304-1328. doi: 10.4236/jamp.2019.76089.