  The Hamiltonian theory for the collective longitudinally polarized colorless
gluon excitations (plasmons) and for collective quark-antiquark excitations
with abnormal relation between chirality and helicity (plasminos) in a
high-temperature quark-gluon plasma (QGP) is developed. For this purpose,
Zakharov's forma\-lism for constructing the wave theory in nonlinear media with
dispersion is used. A generalization of the Poisson superbracket involving both
commuting and anticommuting variables to the case of a continuous medium is
performed and the corresponding Hamilton equations are presented. The canonical
transformations including simultaneously both bosonic and fermionic degrees of
freedom of the collective excitations in QGP are discussed and a complete
system of the canonicity conditions for these transformations is written out.
An explicit form of the effective fourth-order Hamiltonians describing the
elastic scattering of plasmino off plasmino and plasmino off plasmon is found
and the Boltzmann type kinetic equations describing the processes of elastic
scattering are obtained. A detailed comparison of the effective amplitudes
defined within the (pseudo)classical Hamiltonian theory, with the corresponding
matrix elements calcu\-la\-ted early in the framework of high-temperature
quantum chromodynamics in the so-called hard thermal loop approximation is
performed. This enables one to obtain, in particular, an explicit form of the
vertex and coefficient functions in the effective amplitudes and in the
canonical transformations, correspondingly, and also to define the validity of
a purely pseudoclassical approach in the Hamiltonian description of the
dynamics of a quark-gluon plasma. The problem of determining the higher-order
coefficient functions in the canonical transformations of fermionic and bosonic
normal variables is considered.
