References - Bogoliubov Laboratory of Theoretical Physics - JINR

It is clear that the self-adjoint operator rot have fundamental meaning but here we have
only a possibility to find the eigenvalues of this operator. We set P = f rotandforthis
operator polarization the following relations hold valid
P = −M 2 1 − M 2 2 − M 2 3 + N 2 1 + N 2 2 + N 2 3 = −M 2 + N 2 , P 2 = −2(M 2 + N 2 ).
This means that eigenvalues of the polarization operator equal ±p, where p =2, 3, 4, ....
4. Conclusion. In conclusion, we discuss the new situation with solution of spindynamics
equations (6) and (7) and the Maxwell equations (8) and (9). From polynomials
(5) we can construct the orthogonal system of vector fields on S 3 (potential and turbulent).
The coefficients of expansion of the vector and scalar fields over these systems will
be the functions of f. Using the properties of the harmonic polynomials in question we
can derive from the equations of spindynamics and the Maxwell equations the systems
of ordinary differential equations for these coefficients. It is natural to suppose that this
system of equations will have physical solutions only for quite definite meanings of charge
and mass. Thus, at first we have a possibility to find the solution of nonlinear system of
equations that can represent the distinct hadrons and nucleus. It should be noted that
a state of strongly interacting particle is characterized by the following orbital quantum
numbers: 0, 1/2, 1, 3/2 ···.
References
[1] I.B. Pestov, Field Theory and the Essence of Time. Horizons in World Physics, Volume
series 248, Ed. A. Reimer, pp.1-29, (Nova Science, New York 2005); Preprint
of JINR E2–2004–105, Dubna, 2004; ArXiv: gr-qc/0507131.
[2] I.B. Pestov, The concept of Time and Field Theory . Preprint of JINR E2–1996–424,
Dubna, 1996; ArXiv: gr-qc/0308073.
[3] I.B, Pestov, Dark Matter and Potential Fields. Dark Matter: New Research, Ed.
Val Blain, pp. 77-97, (Nova Science, New York, 2005); Preprint of JINR E2–2005–51,
Dubna, 2005; ArXiv: gr-qc/0412096.
[4] I.B. Pestov, Spin and Geometry. Relativistic Nuclear Physics and Quantum Chromodynamics,
Eds: A.N. Sissakian, V.V.Burov, A.I.Malakhov. Proc. of the XVIII
Intern. Baldin Seminar on High Energy Physics Problems (Dubna, September 25-30,
2006).-Dubna: JINR, 2008. -V.2, p.289-299; Self-Organization of Physical Fields and
Spin. Preprint of JINR E2–2008–93, Dubna, 2008, 42p.
[5] G. de Rham, Varietes Differentiables.-Paris: Hermann, 1955.
450