Alberto Strumia
Fundamental fields as eigenvectors of the metric tensor in a 16-dimensional space-time
(82K, LATeX 2e)
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 $V^{n}$. 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 $4${\em -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 $16${\em-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.