Matter and Space-Time

We construct a mathematical theory of matter in space-time. The basic feature is to consider a special 4-dimensional elastic medium where a screw dislocation in the additional (fifth) coordinate causes a field of action over space-time. The properties of this dislocations are the mathematical model for elementary particles. The generated fields are linear in the sources and their squares are proportional to the energy stored in those fields. The waves in 3-D space, in the model, are the propagation of the properties of this field of action and carry energy, momentum and energy-momentum besides the information on the type of matter generating dislocations. If two screw dislocations approach each other their respective fields a and b add up and an interaction energy results from the additional terms in the square of the sum: the energy related to the interaction is the difference between (a + b)2 and a2 + b2, difference that can be negative for attractive interactions, or positive for repulsive interaction.