Nonlinear dynamics of soft boson excitations in hot QCD plasma I: plasmon-plasmon scattering

On the basis of pure gauge sector of Blaizot-Iancu equation, we derive kinetic equation of Boltzmann type, taking into account 2n+2-colorless plasmon decay processes, n=1,2,.... Using so-called Tsytovich correspondence principle, a direct connection between matrix elements of the plasmon decay processes and certain effective current, generating these processes, is established. The procedure of calculation of matrix element for simplest four-plasmon decay is considered comprehensively. The limiting value of the plasmon occupation number (~ 1/g^2, where g is a strong coupling) wherein all plasmon decays with n >= 1, contribute to the right-hand side of the Boltzmann equation, is defined. The iterative method of calculation of matrix elements for higher decay processes (n > 1), is proposed, and a problem of their gauge-invariance is discussed. Proceed from the general reasons the problem of extension of suggested approach to the case of color plasmons, is considered. The explicit form of linearized Boltzmann equation for color plasmons is written out, and it is shown that this equation covariantly conserves the color current, resulting from color-plasmon number density.