An analytical study of the Evolution of the Real time in statistical Quantum mechanics of the Gauge theory (Quarks and Gluons') with the potential expansion until the sixth degree

We take the effective Hamiltonian operator until the sixth degree [18] and this operator has enabled us to convert from gauge theory with group SU(2) into the study of statistical quantum mechanics with the group SU(2) and this mean physically we have converted from the study of an infinite number of particles and of freedom degrees (quarks- gluons-plasma) into study of three particles (Global) independed of space that mains nine of freedom degrees and specifically nine anharmonic oscillators and after that we apply Wigner’s mode [16] on homogenous modes remaining after quantization of the inhomogenous modes and we have concluded the relation of real-time evolution of the color magnetic energy and the color electric energy .