The paper represents the results of the study of the four-dimensional Euclidean space with real time (E-space), where 0 ≤ ||VE|| ≤ ∞, in sub-hadronic physics. This closed space has a metric that distinguished from the Minkowski space and the results obtained in the model are different from physical law in the Minkowski space. As it follows from the model of Lagrangian Mechanics, quarks in the central-symmetric attractive potential, kinetic energy of quark diminishes while the speed grows as the quarks exchange their energy-mass with gluons possessing a zero rest mass, so that to ensure the permanent proton mass. This dependence describes the dynamical relation of constituent and current quarks masses.
In the quantified motion model it has been stated, that the oscillations of the particles are cyclic, including alternating localization and translation phases, the action per cycle for a free particle equals $h$. The calculation of charge distribution density in proton, carried out on the basis of this model, conforms to the results of the experimental research. All relations between physical values in the E-space, mapped in the Minkowski space, correspond to the principles of SR and are Lorentz-covariant and the infinite velocity is equal to the velocity of light in the Minkowski space. These models have a transparent physical sense.
"Guarcs in the Inside Hadronic Four-Dimensional Euclidean Space with Real Time." J. Phys. Math. 6 (2) 1 - 6, 2015. https://doi.org/10.4172/2090-0902.1000140