At the beginning of XX century there were attempts to construct theory of Gravitation. One way to do that was to construct action functional for gravitational field using field theory. It was realized that in order to
obtain conserved energy momentum tensor it is necessary to add infinite number of terms to action and the consistent action was not found [1].
Later, Hilbert and Einstein found the action using geometrization principle. They simply found that the underlying
geometry for gravitation is Riemannian Geometry. And action functional is the scalar curvature of Riemannian
geometry.
After this discovery many scientists tried to geometrize electromagnetism in the same way. For review of them see [2].
We will review the most well known of them, Weyl and Kaluza-Klein theories.
In 1918, H. Weyl proposed a unified model of electromagnetism and gravitation in the framework of modified Riemannian geometry [3]. Weyl considered Riemannian geometry with changing length of a vector. Unfortunately, predictions of Weyl's theory are in contradiction with experimental results as it is discussed in [2] . For example, one of the predictions of it is the following: if one observer goes to the electromagnetic field with higher
potential and comes back to the same place its time is different from the observer's who was all time at the first place.
In 1920's, T. Kaluza proposed a unified model of electromagnetism and gravitation in the framework of Riemannian geometry in 5 -dimensional spacetime. Besides 5-dimensionality this theory has a few difficulties.
It contains unobserved dilaton field, does not reproduce Maxwell equations and equations of motion for a classical particle
interacting with electromagnetic field exactly (charge/mass problem).
From 1920 up to now there were many attempts to solve this problem
in a variety of different approaches. We encourage authors of those papers to send us a brief review of their results. We will add them here.
In 2002, Dr. S. S. Shahverdiyev proposed a unified model in the framework of General geometry.
Results are here
[1] R. Feynman, Lectures on Gravitation
[2] W. Pauli, Theory of Relativity, Pergamon Press, 1958
[3] H. Weyl, Sitzungsber. d. Berl. Acad. 1918 p.465
[4] T. Kaluza, On the Unification Problem in Physics