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Shortly after the postulation of quarks by Zweig and Gell-Mann in 1964 and the experimental confirmation of these subnucleon formations [1,2] in 1969, Feynman, Ravndal and Kislinger (FRK) in 1971 proposed a relativistic three-quark model of nucleons [3] to study the internal structure and state of these dynamical systems and explain a number of thier important properties. The idea of this model is that all three quarks effectively interact with each other through the potential of a four-dimensional harmonic oscillator, which does not allow the system to decay into individual free quarks. Despite the obvious progress in describing the internal motion of nucleons within the framework of this model, we have to state that it is not realistic enough, since continuous processes of gluon exchange between quarks are ignored. To overcome this difficulty, we considered the problem of self-organization of a dynamical quark system immersed in a color gluon thermostat in the framework of the mathematical representation of a complex probabilistic process [4] that satisfies an equation of the Kline-Gordon-Langevin type. Obviously, this is a natural and essential generalization of the FRK nucleon model.
In this work, using the hidden symmetry of the internal motion of a dynamical system, we have developed a mathematical approach that allows us to construct the wave function of the nucleon in the form of a two-fold integral representation, taking into account the relaxation of the quark system in a color gluon thermostat. It should be noted that the generalized model can be especially useful for studying the state of nucleons under critical conditions, which takes place, for example, in massive and dense stellar formations, such as neutron stars, etc.
[1] E. D. Bloom, et al. (1969), High-Energy Inelastic e–p Scattering at 6° and 10°, Physical Review Letters, 23 (16): 930—934.
[2] M. Breidenbach et al. (1969), Observed Behavior of Highly Inelastic Electron–Proton Scattering, Physical Review Letters, 23 (16): 935—939.
[3] R. P. Feynman, M. Kislinger, and F. Ravndal (1971), Current Matrix Elements from a Relativistic Quark Model, Phys. Rev. D3, 2706.
[4] A. S. Gevorkyan, A. V. Bogdanov and V.V. Mareev, Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment, Symmetry 2021, 13, 1546. https://doi.org/10.3390/sym13081546
