Hamiltonian Formalism for Collective Fermionic Waves in a Quark-Gluon Plasma

A Hamiltonian theory has been developed for collective quark-antiquark excitations with abnormal relation between chirality and helicity in a high-temperature quark-gluon plasma (QGP). For this purpose, Zakharov’s formalism for constructing the wave theory in nonlinear media with dispersion has been used. On the basis of this approach, special canonical transformations are derived including simultaneously bosonic and fermionic degrees of freedom of the collective excitations in the QGP. An explicit form of the effective fourth-order Hamiltonian in powers of creation and annihilation operators of plasmons and plasminos describing processes of elastic scattering of plasminos off plasminos and plasminos off plasmons has been found. The developed approach has been used to construct the Boltzmann-type kinetic equation describing the process of elastic scattering of plasminos off plasminos in the quark-gluon plasma and the effect of the so-called nonlinear Landau damping of soft Fermi excitations. The effective amplitude of plasmino-plasmino interaction defined in the context of the classical Hamiltonian theory has been compared with the corresponding matrix element obtained in the framework of high-temperature quantum chromodynamics in the so-called hard thermal loop approximation. This has enabled us to obtain an explicit form of the vertex and coefficient functions in the effective amplitudes and in the canonical transformations.