arXiv subjects

A. I. Bondarenko

Publications and source records attributed to A. I. Bondarenko.

5 recordsLinked to original sources

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↗

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↗

arXiv2011

Coherent Dissociation $^{16}$O~$\rightarrow$~4$α$ in Photoemulsion at an Incident Momentum of 4.5 GeV/$c$ per Nucleon

First searches for the coherent dissociation of relativistic oxygen nuclei into four a particles are reported. It is shown that reactions of this type are characterized by a significantly lower decay temperature than the conventional multifragmentation of residual projectile nuclei. The momentum spectra and correlations of a panicles are not reproduced by the simple statistical model of direct fragmentation. The possibility that the oxygen nucleus undergoing fragmentation acquires a nonzero angular momentum in the collision process is discussed.

nucl-ex↗