The study of analytical for evolution of real times in quantum mechanic for gauge theory for quarks-gluons plasma with su (3) with antiperiodic conditions group by using perturbation theory

We take the effective Hamiltonian operator until the four degree[3] and this operator has enabled us to convert from pure gauge theory with group SU(3)With antiperiodic conditions into the quantum mechanics with the group SU(3) With antiperiodic conditionsand this mean physically we have converted from the study of an infinite number of particles and of freedom degrees (quarks- gluens-plasma) into study of eight particles (Global)independent of space that mainsTwenty-four of freedom degrees and specificallyTwenty-four inharmonic oscillators and after that we apply perturbation theory (that of the depend of creation operator 〖D ̂^+〗_i^a and annihilation operator D ̂_i^a) on homogenous modes remaining after quantization of the inhomogeneous modes and we have concluded the relations: 1-The time evolution for the ensemble average of global operator square (the color magnetic energy B ̂_i^a B ̂_i^a). 2-Thetime evolution for the ensemble average of impulse operator square (the color electric energy Π ̂_i^a Π ̂_i^a).