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Yu. A. Markov

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

At least 19 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 $c^{\phantom{\ast}(α)a}_{\bf k},\,α= 1, 2$, of the new normal field variable $c^{\,a}_{\bf k}$ and in the new color charges ${\mathcal Q}^{a}_α$ 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 ${\mathcal N}^{\,(α,α^{\prime})aa^{\prime}_{\phantom{1}}}_{\bf k}(τ)$, 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.

hep-th↗
arXiv2026

Canonical formulation of the plasmon - hard particle scattering process in a quark-gluon plasma

It is shown that the Hamiltonian formalism proposed previously in [1] to describe the nonlinear dynamics of only {\it soft} fermionic and bosonic excitations contains much more information than initially assumed. In this paper, we have demonstrated in detail that it also proved to be very appropriate and powerful in describing a wide range of other physical phenomena, including the scattering of colorless plasmons off {\it hard} thermal (or external) color-charged particles moving in a hot quark-gluon plasma. A generalization of the Poisson superbracket including both anticommuting variables for hard modes and normal variables of the soft Bose field, is presented for the case of continuous medium. The corresponding Hamilton equations are defined, and the most general form of the third- and fourth-order interaction Hamiltonians is written out in terms of the normal boson field variables and hard momentum modes of the quark-gluon plasma. The canonical transformations involving both bosonic and hard mode degrees of freedom of the system under consideration, are discussed. The canonicity conditions for these transformations based on the Poisson superbracket, are derived. The most general structure of canonical transformations in the form of integro-power series up to sixth order in a new normal field variable and a new hard mode variable, is presented. For the hard momentum mode of quark-gluon plasma excitations, an ansatz separating the color and momentum degrees of freedom, is proposed. The question of approximation of the total effective scattering amplitude when the momenta of hard excitations are much larger than those of soft excitations of the plasma, is considered. 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.

hep-th↗
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.

hep-th↗
arXiv2024

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.

hep-th↗
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.

hep-th↗
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.

hep-th↗
arXiv2020

Path integral representation for inverse third order wave operator within the Duffin-Kemmer-Petiau formalism. I

Within the framework of the Duffin-Kemmer-Petiau (DKP) formalism with a deformation, an approach to the construction of the path integral representation in parasuperspace for the Green's function of a spin-1 massive particle in external Maxwell's field is developed. For this purpose a connection between the deformed DKP-algebra and an extended system of the parafermion trilinear commutation relations for the creation and annihilation operators $a^{\pm}_{k}$ and for an additional operator $a_{0}$ obeying para-Fermi statistics of order 2 based on the Lie algebra $\mathfrak{so}(2M+2)$ is established. The representation for the operator $a_{0}$ in terms of generators of the orthogonal group $SO(2M)$ correctly reproducing action of this operator on the state vectors of Fock space is obtained. An appropriate system of the parafermion coherent states as functions of para-Grassmann numbers is introduced. The procedure of the construction of finite-multiplicity approximation for determination of the path integral in the relevant phase space is defined through insertion in the kernel of the evolution operator with respect to para-supertime of resolutions of the identity. In the basis of parafermion coherent states a matrix element of the contribution linear in covariant derivative $\hat{D}_μ$ to the time-dependent Hamilton operator $\hat{\cal H}(τ)$, is calculated in an explicit form. For this purpose the matrix elements of the operators $a^{\phantom{2}}_0$, $a_{0}^{2}$, the commutators $[\hspace{0.03cm}a^{\phantom{\pm}\!}_{0}, a^{\pm}_{n}\hspace{0.02cm}]$, $[\hspace{0.03cm}a^{2}_{0}, a^{\pm}_{n}\hspace{0.02cm}]$, and the product $\hat{A}\hspace{0.03cm}[\hspace{0.03cm}a^{\phantom{\pm}\!}_{0}, a^{\pm}_{n}\hspace{0.02cm}]$ with $\hat{A} \equiv\exp\hspace{0.02cm}\bigl(-i\frac{2π}{3}\,a_{0}\bigr)$, were preliminary defined.

hep-th↗
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.

hep-th↗
arXiv2020

Path integral representation for inverse third order wave operator within the Duffin-Kemmer-Petiau formalism. II

This paper is an immediate continuation of the first part of our paper [1]. Here, in a para-Grassmann algebra we introduce a noncommutative, associative star product $*$ (the Moyal product), which is a direct generalization of the star product in the algebra of Grassmann numbers. Isomorphism between the algebra of para-Grassmann numbers of order 2 equipped with the star product and with the algebra of creation and annihilation operators $a_{n}^{\pm}$ obeying the para-Fermi statistics of the same order is established. Two independent approaches to the calculation of the Moyal product $*$ are considered. It is shown that in calculating the matrix elements in the basis of parafermion coherent states of various expressions it should be taken into account constantly that we work in the so-called Ohnuki and Kamefuchi's generalized state-vector space $\mathfrak{U}_{\;G}$, whose state vectors include para-Grassmann numbers $ξ_{k}$ in their definition, instead of the standard state-vector space $\mathfrak{U}$ (the Fock space). Otherwise, the wide array of contradictions arises. An immediate consequence of using the extended state-vector space $\mathfrak{U}_{\;G}$ is a necessity to consider the quadratic Casimir operators $\hat{C}_{2}$ and $\hat{C}_{2}^{\prime}$ of the orthogonal groups $SO(2M)$ and $SO(2M + 1)$, correspondingly. The action rules of the Casimir operators on the state vectors, an explicit form of their matrix elements are defined and a more general connection between the Harish-Chandra operator $\hatω^2$ and the Geyer operator $a_{0}^{2}$ is obtained. The notions of the triple star product, the star exponent and the Moyal bracket are introduced.

hep-th↗
arXiv2018

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 $ϕ_{a}$ and $ϕ_{b}$ into identity. The way of incorporating para-Grassmann numbers $ξ_{k}$ 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 $ξ_{k}$ 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.

math-ph↗
arXiv2017

Fourth order wave equation in Bhabha-Madhavarao spin-$\frac{3}{2}$ theory

Within the framework of the Bhabha-Madhavarao formalism, a consistent approach to the derivation of a system of the fourth order wave equations for the description of a spin-$\frac{3}{2}$ particle is suggested. For this purpose an additional algebraic object, the so-called $q$-commutator ($q$ is a primitive fourth root of unity) and a new set of matrices $η_μ$, instead of the original matrices $β_μ$ of the Bhabha-Madhavarao algebra, are introduced. It is shown that in terms of the $η_μ$ matrices we have succeeded in reducing a procedure of the construction of fourth root of the fourth order wave operator to a few simple algebraic transformations and to some operation of the passage to the limit $z \rightarrow q$, where $z$ is some (complex) deformation parameter entering into the definition of the $η$-matrices. In addition, a set of the matrices ${\cal P}_{1/2}$ and ${\cal P}_{3/2}^{(\pm)}(q)$ possessing the properties of projectors is introduced. These operators project the matrices $η_μ$ onto the spins 1/2- and 3/2-sectors in the theory under consideration. A corresponding generalization of the obtained results to the case of the interaction with an external electromagnetic field introduced through the minimal coupling scheme is carried out. The application to the problem of construction of the path integral representation in parasuperspace for the propagator of a massive spin-$\frac{3}{2}$ particle in a background gauge field within the Bhabha-Madhavarao approach is discussed.

hep-th↗
arXiv2015

Third order wave equation in Duffin-Kemmer-Petiau theory. Massive case

Within the framework of the Duffin-Kemmer-Petiau (DKP) formalism a more consistent approach to the derivation of the third order wave equation obtained earlier by M. Nowakowski [Phys.Lett.A {\bf 244} (1998) 329] on the basis of heuristic considerations is suggested. For this purpose an additional algebraic object, the so-called $q$ - commutator ($q$ is a primitive cubic root of unity) and a new set of matrices $η_μ$ instead of the original matrices $β_μ$ of the DKP algebra are introduced. It is shown that in terms of these $η_μ$ matrices we have succeeded in reducing a procedure of the construction of cubic root of the third order wave operator to a few simple algebraic transformations and to a certain operation of the passage to the limit $z \rightarrow q$, where $z$ is some complex deformation parameter entering into the definition of the $η$ - matrices. A corresponding generalization of the result obtained to the case of the interaction with an external electromagnetic field introduced through the minimal coupling scheme is carried out and a comparison with M. Nowakowski's result is performed. A detailed analysis of the general structure for a solution of the first order differential equation for the wave function $ψ(x; z)$ is performed and it is shown that the solution is singular in the $z \rightarrow q$ limit. The application to the problem of construction within the DKP approach of the path integral representation in parasuperspace for the propagator of a massive vector particle in a background gauge field is discussed.

hep-th↗
arXiv2008

Nonlinear dynamics of soft fermion excitations in hot QCD plasma III: Soft-quark bremsstrahlung and energy losses

In general line with our early works [Yu.A. Markov, M.A. Markova, Nucl. Phys. A770 (2006) 162; 784 (2007) 443] within the framework of a semiclassical approximation the general theory of calculation of effective currents and sources generating bremsstrahlung of an arbitrary number of soft quarks and soft gluons at collision of a high-energy color-charged particle with thermal partons in a hot quark-gluon plasma, is developed. For the case of one- and two-scattering thermal partons with radiation of one or two soft excitations, the effective currents and sources are calculated in an explicit form. In the model case of `frozen' medium, approximate expressions for energy losses induced by the most simple processes of bremsstrahlung of soft quark and soft gluon, are derived. On the basis of a conception of the mutual cancellation of singularities in the sum of so-called `diagonal' and `off-diagonal' contributions to the energy losses, an effective method of determining color factors in scattering probabilities, containing the initial values of Grassmann color charges, is suggested. The dynamical equations for Grassmann color charges of hard particle used by us early are proved to be insufficient for investigation of the higher radiative processes. It is shown that for correct description of these processes the given equations should be supplemented successively with the higher-order terms in powers of the soft fermionic field.

hep-ph↗
arXiv2006

Nonlinear dynamics of soft fermion excitations in hot QCD plasma II: Soft-quark - hard-particle scattering and energy losses

In general line with our first work [Yu.A. Markov, M.A. Markova, Nucl. Phys. A 770 (2006) 162] within the framework of semiclassical approximation a general theory for the scattering processes of soft (anti)quark excitations off hard thermal particles in hot QCD-medium is thoroughly considered. The dynamical equations describing evolution for the usual classical color charge $Q^a(t)$ and Grassmann color charges $θ^i(t), θ^{\dagger i}(t)$ of hard particle taking into account the soft fermion degree of freedom of the system are suggested. On the basis of these equations and the Blaizot-Iancu equations iterative procedure of calculation of effective currents and sources generating the scattering processes under consideration is defined and their form up to third order in powers of free soft quark field, soft gluon one, and initial values of the color charges of hard particle is explicitly calculated. With use of the generalized Tsytovich principle a connection between matrix elements of the scattering processes and the effective currents and sources is established. In the context of the effective theory suggested for soft and hard fermion excitations new mechanisms of energy losses of high-energy parton propagating through QCD-medium are considered.

hep-ph↗
arXiv2006

Nonlinear dynamics of soft fermion excitations in hot QCD plasma I: soft-quark - soft-gluon scattering

Within the framework of the hard thermal loop effective theory we derive a system of Boltzmann-like kinetic equations taking into account the simplest processes of nonlinear interaction of soft fermionic and bosonic QCD plasma excitations: elastic scattering of soft-(anti)quark excitations off soft-gluon and soft-quark excitations, pair production of soft quark-antiquark excitations, annihilation into two soft-gluon excitations. The matrix elements of these processes to leading order in the coupling constant $g$ are obtained. The iterative method of calculation of the matrix elements for the higher processes of soft-mode interactions is proposed. The most general expression for the emitted radiant power induced by the effective currents and effective sources in a quark-gluon plasma (QGP) taking into account an existence of fermion sector of plasma excitations is defined. The explicit form of the linearized Boltzmann equation accounting for scattering of color(less) plasminos off color(less) plasmons is written out.

hep-ph↗
arXiv2005

Scattering of high-energy partons off ultrasoft gluon fluctuations in hot QCD plasma and energy losses

Within the framework of the effective theory for ultrasoft field modes a problem of interacting an energetic color particle with ultrasoft fluctuations in hot gluon plasma is considered. The procedure of calculation of certain effective current generating the process of interaction is proposed, and the problem of its gauge independence is discussed. The application of the theory developed to the problem of energy losses of the energetic color particle propagating through hot QCD-medium is given. It is shown that the perturbation approach for calculation of energy losses breaks down at the ultrasoft momentum scale of plasma excitations.

hep-ph↗
arXiv2005

Nonlinear dynamics of soft boson collective excitations in hot QCD plasma III: bremsstrahlung and energy losses

Within of the framework of semiclassical approximation a general formalism for deriving an effective current generating bremsstrahlung of arbitrary number of soft gluons (longitudinal or transverse ones) in scattering of higher-energy parton off thermal parton in hot quark-gluon plasma with subsequent extension to two and more scatterers, is obtained. For the case of static color centers an expression for energy loss induced by usual bremsstrahlung of lowest-order with allowance for an effective temperature-induced gluon mass and finite mass of the projectile (heavy quark), is derived. The detailed analysis of contribution to radiation energy loss associated with existence of effective three-gluon vertex induced by hot QCD medium, is performed. It is shown that in general, the bremsstrahlung associated with this vertex have no sharp direction (as in the case of usual bremsstrahlung) and therefore here, we can expect an absence of suppression effect due to multiple scattering. For the case of two color static scattering centers it was shown that the problem of calculation of bremsstrahlung induced by four-gluon hard thermal loop (HTL) vertex correction can be reduced to the problem of the calculation of bremsstrahlung induced by three-gluon HTL correction. It was shown that for limiting value of soft gluon occupation number $N_{\bf k}\sim 1/α_s$ all higher processes of bremsstrahlung of arbitrary number of soft gluons become of the same order in coupling, and the problem of resummation of all relevant contributions to radiation energy loss of fast parton, arises. An explicit expression for matrix element of two soft gluon bremsstrahlung in small angles approximation is obtained.

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