  We have developed the Hamiltonian theory for collective longitudinally
polarized colorless excitations (plasmons) in a high-temperature gluon plasma
using the general formalism for constructing the wave theory in nonlinear media
with dispersion, which was developed by V.E. Zakharov. In this approach, we
have explicitly obtained a special canonical transformation that makes it
possible to simplify the Hamiltonian of interaction of soft gluon excitations
and, hence, to derive a new effective Hamiltonian. The approach developed here
is used for constructing a Boltzmann-type kinetic equation describing elastic
scattering of collective longitudinally polarized excitations in a gluon plasma
as well as the effect of the so-called nonlinear Landau damping. We have
performed detailed comparison of the effective amplitude of the plasmon-plasmon
interaction, which is determined using the classical Hamilton theory, with the
corresponding matrix element calculated in the framework of high-temperature
quantum chromodynamics; this has enabled us to determine applicability limits
for the purely classical approach described in this study.
