Russian Physics Journal

, Volume 61, Issue 2, pp 337–346 | Cite as

E-Invariant Quantized Motion of Valence Quarks

  • E. L. Kreymer

In sub-proton space wave processes are impossible. The analog of the Klein–Gordon equation in sub-proton space is elliptical and describes a stationary system with a constant number of particles. For dynamical processes, separation of variables is used and in each quantum of motion of the quark two states are distinguished: a localization state and a translation state with infinite velocity. Alternation of these states describes the motion of a quark. The mathematical expectations of the lifetimes of the localization states and the spatial extents of the translation states for a free quark and for a quark in a centrally symmetric potential are found. The action after one quantum of motion is equal to the Planck constant. The one-sided Laplace transform is used to determine the Green’s function. Use of path integrals shows that the quantized trajectory of a quark is a broken line enveloping the classical trajectory of oscillation of the quark. Comparison of the calculated electric charge distribution in a proton with its experimental value gives satisfactory results. A hypothesis is formulated, according to which the three Grand Geometries of space correspond to the three main interactions of elementary particles.


separation of variables states of motion of a quark quantized motion Green’s functions hypothesis 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • E. L. Kreymer
    • 1
  1. 1.CarmelIsrael

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