Model of Four-Dimensional Sub-Proton Euclidean Space with Real Time for Valence Quarks. Lagrangian Mechanics

The model of Euclidean space with imaginary time used in sub-hadron physics uses only part of it since this part is isomorphic to Minkowski space and has the velocity limit 0 ≤ ||v_Ei|| ≤ 1. The model of four-dimensional Euclidean space with real time (Е space), in which 0 ≤ ||v_E|| ≤ ∞ is investigated. The vectors of this space have Е-invariants, equal or analogous to the invariants of Minkowski space. All relations between physical quantities in Е-space, after they are mapped into Minkowski space, satisfy the principles of SRT and are Lorentz-invariant, and the velocity of light corresponds to infinite velocity. Results obtained in the model are different from the physical laws in Minkowski space. Thus, from the model of the Lagrangian mechanics of quarks in a centrally symmetric attractive potential it follows that the energy-mass of a quark decreases with increase of the velocity and is equal to zero for v = ∞. This made it possible to establish the conditions of emission and absorption of gluons by quarks. The effect of emission of gluons by high-energy quarks was discovered experimentally significantly earlier. The model describes for the first time the dynamic coupling of the masses of constituent and current quarks and reveals new possibilities in the study of intrahardon space. The classical trajectory of the oscillation of quarks in protons is described.