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.
Highlights
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 (n-dimensional “vierbein”)
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
Our proposal is based on the idea of associating each fundamental interaction field with a vector potential which is an eigenvector of the metric tensor of a multidimensional space-time manifold V n (n-dimensional “vierbein”)
Summary
Our proposal is based on the idea of associating each fundamental interaction field with a vector potential which is an eigenvector of the metric tensor of a multidimensional space-time manifold V n (n-dimensional “vierbein”). It is relevant to observe that within an n-dimensional space-time, the metric tensor, when represented onto the basis of its eigenvectors, yields a connection involving a 2-index antisymmetric tensor of the same form as a non-Abelian Maxwell tensor which may be related to the fundamental interaction fields in a quite natural way. A complete presentation of the theory and much more has been proposed in my book [11]
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