arXiv subjects

N. Yu. Markov

Publications and source records attributed to N. Yu. Markov.

6 recordsLinked to original sources

arXiv2026

Hamiltonian formalism for Bose excitations in a plasma with a non-Abelian interaction: plasmon bremsstrahlung

The classical Hamiltonian wave theory describing plasmon bremsstrahlung radiation occurring upon collision of high-energy color-charged particles in a hot quark-gluon plasma is proposed. A generalization of the Lie-Poisson bracket to the case of a hot QCD medium, involving two independent components $a^{\phantom{\ast}(1)a}_{\bf k}$ and $a^{\phantom{\ast}(2)a}_{\bf k}$ of the bosonic normal field variable $a^{\phantom{\ast}a}_{\bf k}$ and two non-Abelian color charges $Q^{\,a}_1$ and $Q^{\,a}_2$ is suggested. The canonical transformations including both bosonic degrees of freedom of the soft collective excitations of the hot quark-gluon plasma and degrees of freedom of two hard test particles related to their color charges are written out. The most general structure of the canonical transformations in the form of integro-power series in the components $c^{\phantom{\ast}(\alpha)a}_{\bf k},\,\alpha = 1, 2$, of the new normal field variable $c^{\,a}_{\bf k}$ and in the new color charges ${\mathcal Q}^{a}_{\alpha}$ up to the terms of sixth order is presented. To construct kinetic equations the multiple-time-scale perturbation theory is used. The notion of the plasmon number density ${\mathcal N}^{\,(\alpha,\alpha^{\prime})aa^{\prime}_{\phantom{1}}}_{\bf k}(\tau)$, which is a nontrivial matrix both in the effective color space and in effective two-particle space, is introduced. The self-consistent system of four Boltzmann-type kinetic equations taking into account the time evolution of the averaged color charges of the hard particles is obtained. In the approximation of the fixed color charges of two interacting particles the exact solution of the system of kinetic equations defining the dynamics of the colorless $N^{(1)}_{\bf k}$, $W^{(1)}_{\bf k}$ and color $N^{(2)}_{\bf k}$, $W^{(2)}_{\bf k}$ components of the plasmon number density, is obtained.

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arXiv2025

Classical scattering matrix for hard and soft Bose-excitations in a non-Abelian plasma within the Hamiltonian formalism

Within the framework of the Zakharov-Schulman approach, in close analogy with the methods of quantum field theory, the classical scattering matrix for the simplest process of interaction between hard and soft excitations in a quark-gluon plasma (QGP), is determined. The classical $\mathcal{S}$-matrix is defined in the form of the most general integro-power series expansion in the asymptotic values as $t\rightarrow-\infty$ of normal bosonic variables $c^{-\,a}_{\hspace{0.02cm}{\bf k}}(t)$ and $(c^{-\,a}_{\hspace{0.02cm}{\bf k}}(t))^{\ast}$, describing the soft gluon excitations of the system, and a color charge $\mathcal{Q}^{-\hspace{0.03cm}a}(t)$ of a hard particle. The first nontrivial contribution to this matrix is calculated. The quantum commutator of quantum field operators is replaced by the so-called Lie-Poisson bracket depending on the classical asymptotic variables. The developed approach is used to derive a general formula for energy loss of a fast color-charged particle during its scattering off soft bosonic excitations of QGP in the framework of the classical Hamiltonian formalism. For this purpose, the notion of an effective current of the scattering process under consideration is introduced and its relation to the classical $\mathcal{S}$-matrix is determined. With the help of the known form of the classical scattering matrix, the desired effective current is recovered, which in turn allowed us to determine the formula for energy loss of the hard color particle. The rough estimates of energy loss at the order-of-magnitude level is provided and their comparison with the well-known results on the radiation and collision losses is performed.

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arXiv2023

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

Hamiltonian theory for collective longitudinally polarized gluon excitations (plasmons) interacting 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 $a^{\hspace{0.03cm}a}_{{\bf k}}$ 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 ${\mathcal N}^{\hspace{0.03cm}aa^{\prime}_{\phantom{1}}\!}_{{\bf k}}$, which is a nontrivial matrix in the color space, is introduced. An explicit form of the effective fourth-order Hamiltonian describing the elastic scattering of a 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 the interaction of two infinitely narrow wave packets is considered. A system of nonlinear first-order ordinary differential equations defining the dynamics of the interaction of the colorless $N^{\hspace{0.01cm}l}_{\bf k}$ and color $W^{\hspace{0.01cm}l}_{\bf k}$ 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 $a^{\hspace{0.03cm}a}_{{\bf k}}$ and color charge $Q^{a}$ is discussed.

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arXiv2023

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 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.

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arXiv2022

Superparticle in an external chiral matter superfield

In this paper the interaction Lagrangian of a superparticle with an external chiral superfield $Φ(x,θ,\barθ)$,invariant with respect to the global supersymmetry, is proposed. The kinematics of the superparticle is defined in an extended superspace described by superspace coordinates $(x_μ,θ_α,\barθ_α)$, where $x_μ$ are pure bosonic coordinates, $μ=0,\ldots,3$; $θ_α$ and $\barθ_α$ are additional fermionic Grassmann-valued spinors. With the purpose of the construction of the required Lagrangian, chiral analogues of the supervector $A_μ(x,θ,\barθ)$ and superspinor $A_α(x,θ,\barθ)$, $\bar{A}_{\dotα}(x,θ,\barθ)$ gauge fields are introduced, which are also matrices in color space. The problem considered in this paper is the further step in deriving the dynamical equations of motion for a spin color-charged particle moving in an external fermionic matter field. These equations of motion are of fundamental importance, for example, when taking into account the influence of fermionic background fields induced in a hot quark-gluon plasma (QGP) by thermal fluctuations on the dynamics of hard color-charged partons crossing the QGP. In turn, the solution of this problem will make it possible, at least at the qualitative level, to advance in the study of the motion in the external fermion matter field of such a complex physical object as a string.

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arXiv2020

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

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.

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