Description of Fermions Interacting with Two Calibration Fields Based on Cartan Mechanics

Here traditional quantum mechanics was used and the probability of scattering and absorption of photons by the fermion system was calculated. Today it is already clear that the theory of color or nuclear interaction can be constructed by analogy with the electro-weak interaction, which describes the electromagnetic and weak interaction of elementary particles. For this purpose, quantum field theory can be used. In this paper, the interaction of fermions with 2 gauge fields is described on the basis of the mechanic E. Cartan. The dynamics of fermions and gauge fields is also described. The Hilbert-Einstein equations for the gravitational field are also formulated. On this basis, a mathematical model of the Big Bang is proposed - the transformation of inflaton into a system of particles and antiparticles, and their annihilation with heating of the remaining particles.