Unitary quantization and para-Fermi statistics of order two

A connection between a unitary quantization scheme and para-Fermi statistics of order 2 is considered. An appropriate extension of Green's ansatz is suggested. This extension allows one to transform bilinear and trilinear commutation relations for the annihilation and creation operators of two different para-Fermi fields $\phi_{a}$ and $\phi_{b}$ into identity. The way of incorporating para-Grassmann numbers $\xi_{k}$ into a general scheme of uniquantization is also offered. For parastatistics of order 2 a new fact is revealed, namely, the trilinear relations containing both the para-Grassmann variables $\xi_{k}$ and the field operators $a_{k}$, $b_{m}$ under a certain invertible mapping go over into the unitary equivalent relations, where commutators are replaced by anticommutators and vice versa. It is shown that the consequence of this circumstance is the existence of two alternative definitions of the coherent state for para-Fermi oscillators. The Klein transformation for Green's components of the operators $a_{k}$, $b_{m}$ is constructed in an explicit form that enables us to reduce the initial commutation rules for the components to the normal commutation relations of ordinary Fermi fields. A nontrivial connection between trilinear commutation relations of the unitary quantization scheme and so-called Lie-supertriple system is analysed. A brief discussion of the possibility of embedding the Duffin-Kemmer-Petiau theory into the unitary quantization scheme is provided.Comment: 44 pages, the version published in J. Exp. Theor. Phy

Problem of the noise-noise correlation function in hot non-Abelian plasma

In this work on the basis of Kadomtsev's kinetic fluctuation theory we present the more general expression for noise-noise correlation function in effective theory for ultrasoft field modes.Comment: 3 pages, REVTeX

Hamiltonian formalism for Fermi excitations in a plasma with a non-Abelian interaction

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 formalism 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 calculated 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.Comment: 69 pages, 2 figures, typos corrected and references adde

Hamiltonian formalism for Bose excitations in a plasma with a non-Abelian interaction I: plasmon -- hard particle scattering

The Hamiltonian theory for the collective longitudinally polarized gluon excitations (plasmons) coupling with classical high-energy test color-charged particle propagating through a high-temperature gluon plasma is developed. A generalization of the Lie-Poisson bracket to the case of a continuous medium involving bosonic normal field variable $a^{\phantom{\ast}\!\!a}_{\hspace{0.03cm}{\bf k}}$ and a non-Abelian color charge $Q^{\hspace{0.03cm}a}$ is performed and the corresponding Hamilton equations are presented. The canonical transformations including simultaneously both bosonic degrees of freedom of the soft collective excitations and degree of freedom of hard test particle connecting with its color charge in the hot gluon plasma are written out. A complete system of the canonicity conditions for these transformations is derived. The notion of the plasmon number density ${\mathcal N}^{a\hspace{0.03cm}a^{\prime}_{\phantom{1}}\!}_{{\bf k}}$, which is a nontrivial matrix in the color space, is introduced. An explicit form of the effective fourth-order Hamiltonian describing elastic scattering of plasmon off a hard color particle is found and the self-consistent system of Boltzmann type kinetic equations taking into account the time evolution of the mean value of the color charge of the hard particle is obtained. On the basis of these equations, a model problem of interaction of two infinitly narrow wave packets is considered. A system of nonlinear first-order ordinary differential equations defining the dynamics of the interaction of the colorless $N^{l}_{\bf k}$ and color $W^{l}_{\bf k}$ components of the plasmon number density is derived. The problem of determining the third- and fourth-order coefficient functions entering into the canonical transformations of the original bosonic variable $a^{\phantom{\ast}\!\!a}_{{\bf k}}$ and color charge $Q^{\hspace{0.03cm}a}$ is discussed.Comment: 57 pages, 5 figure