The Boltzmann equation for colourless plasmons in hot QCD plasma. Semiclassical approximation

Abstract

Within the framework of the semiclassical approximation, we derive the Boltzmann equation describing the dynamics of colorless plasmons in a hot QCD plasma. The probability of the plasmon-plasmon scattering at the leading order in the coupling constant is obtained. This probability is gauge-independent at least in the class of the covariant and temporal gauges. It is noted that the structure of the scattering kernel possesses important qualitative difference from the corresponding one in the Abelian plasma, in spite of the fact that we focused our study on the colorless soft excitations. It is shown that four-plasmon decay is suppressed by the power of g relative to the process of nonlinear scattering of plasmons by thermal particles at the soft momentum scale. It is stated that the former process becomes important in going to the ultrasoft region of the momentum scale.

Nonlinear Dynamics of Soft Boson Excitations in Hot QCD Plasma. I. Plasmon–Plasmon Scattering

“…However, as was shown in Ref. [6], the terms in the decomposition do not all associate with the processes of plasmon decays. The decomposition of averaging free field amplitudes into the correlators containing the pair of complexconjugate potentials or one of the nonconjugate potentials between the inside of the angular brackets of statistical averaging does not give a contribution to the processes of interest to us.…”

“…[6]. There are no new results to be reported here, and they are given for coherent and complete subsequent discussion.…”

“…We have already mentioned it in Ref. [6]. Here, this approach will be developed as applied to the general case of a (2n + 2)-plasmon decay.…”

“…[6]). A more powerful and more convenient tool to derive relativistic Boltzmann equations from exact field Schwinger-Dyson equations, the so-called closed-time-path (CTP) formalism of nonequilibrium quantum-field theory, is considered.…”

“…1 Therefore this system is the most convenient and optimal starting point for the derivation of transport equations for soft plasma excitations. In our previous paper [6] it was shown how, by starting from similar dynamic equations, one can derive a collision term for elastic scattering of two colorless plasmons. However, as was mentioned above, the direct approach presented there is very cumbersome and complicated to extend to the processes of collisions with accounts of many colorless plasmons.…”