System of Particles and Field in a Unified Field Theory

In previous contributions I have presented a unified theory of particles and field, in the Geometry of General Relativity, which accounts for all the known force fields, as well as the properties of elementary particles, without the need to invoke additional dimension or special physical phenomenon. In this paper the theory is fully detailed, and its focus is on models of systems of elementary particles interacting with the field. The equations are established for continuous systems and solutions, as well as methods to solve the usual cases are exposed in the model of 2 particles. It is then possible to build clear models of systems such as nuclei and atoms and study the conditions for their stability. It gives also another vision of the special behavior of the nuclear forces. Discontinuous processes involve discontinuities in the field and I show that they can be represented by particles-like objects, the bosons. Their interaction with particles is formalized in a rigorous but simple way.