References - Bogoliubov Laboratory of Theoretical Physics - JINR

State of hadron matter is defined the operators Mν, Nν, D and the well-known homogenous
harmonic polynomials
�
k
D j mn (q1, q2, q3, q4) = � (j + m)!(j − m)!(j + n)!(j − n)! ×
(−1) m+k (q1 + iq2) m−n+k (q1 − iq2) k (q3 + iq4) j−m−k (q3 − iq4) j+n−k
(m − n + k)!k!(j − m − k)!(j + n − k)!
that form the full orthogonal system of functions on S 3 and are the eigenfunctions of these
operators.
It is almost evident that the equations of spindynamics corresponding to the first
causal structure describe the so-called electroweak interactions and in the second case
these equations describe the strong interactions. Confinement actually means a new
physical situation that arises together with new causal structure.
Now we write the equations of spindynamics (2) and (3) taking into account equation
(4):
1 3
(D + f 2
1 3 (D + f 2
1 3
(D + f 2
1 3 (D + f 2
1 3 (D + f 2
1 3 (D + f 2
1 3 (D + f 2
1 3
(D + f 2
where the operator D is defined as follows
)κ =divK−mμ )λ =divL−mν )μ =divM + mκ
)ν =divN + mλ
)K = −rot L +gradκ + m M
)L =rotK +gradλ + m N
)M =rotN +gradμ−mK )N = −rot M +gradν−mL, ∂ ∂ ∂ ∂
D = q1 + q2 + q3 + q4
∂q1 ∂q2 ∂q3 ∂q4
¿From the first principles it is clear that equations of spindynamics (6) and (7) represent
quantum mechanics of strongly interacting particles.
To complete the picture, we write the Maxwell equations in the form that corresponds
to the second causal structure
where
then
1
(D +2)H = −rot E,
f
Ei = qk
f Fik, Hi = qk
f
(5)
(6)
(7)
1
(D +2)E =rotH, (8)
f
q · E = q · H =0, div E =divH =0, (9)
∗
F ik, Fij = ∂iAj − ∂jAi,
We recognize that if vector field M is a solution to the equation
rot M = p M,
t · M =0, div M =0.
449
∗
F ij= 1
2 eijklF kl .