arXiv subjects

G. V. Efimov

Publications and source records attributed to G. V. Efimov.

At least 19 recordsLinked to original sources

arXiv2013

Elastic scattering and path integral

Representation of the elastic scattering amplitude in the form of the path integral is obtained using the stationary Schroedinger equation. A few methods of evaluation of path integrals for large coupling constants are formulated. The methods are based on the uncertainty correlation. The scattering lengths and cross sections are calculated for the right angled and singular potentials and the Yukawa potential. The comparison with exact results is made.

math-ph↗

arXiv2012

Canonical Quantization of the tachyon field

The canonical quantization of the tachyon field is suggested. Quantization is based on the conception of stable and unstable components of the tachyon degrees of freedom.

hep-ph↗

arXiv2010

QED and ortho-para- positronium mass difference

Bound state problem in the relativistic QED is investigated by the functional integral methods. The ortho- para- positron mass difference is calculated. Contribution of the "nonphysical"$~$ time variable turned out to be important and leads to the nonanalytic dependence of the bound state mass of the order $α^{2\over3}$. It is shown that the relativistic and non-relativistic QED gives different results for this mass shift. In addition so-called abnormal states as "time excitations" arise. Sequential application of relativistic QED to bound state problem is in contradiction with real ortho- and para- positronium bound states. The conclusion: the relativistic QED is not suited to describe real bound states correctly.

hep-ph↗

arXiv2008

On ortho-positronium and gauge

Binding energy of the $1^-$ state (ortho-positronium) in QED is calculated using the one-photon exchange Bethe-Salpeter equation in the Feynman and Coulomb gauges for different coupling constants $α$. Calculations show there is a remarkable difference in values of the binding energy for different coupling constants in these two gauges.

hep-ph↗

arXiv2005

On meson masses

It is shown that in the framework of analytical confinement, when quark and gluon propagators are induced by an vacuum selfdual gluon field with constant strength, the masses of meson with quantum numbers $Q=J^P$ and quark constituents $m_1,~m_2$ are described with reasonable accuracy by the formula $$ M_Q(m_1,m_2)=(m_1+m_2)[1+{A_Q\over (m_1^2+1.13m_1m_2+m_2^2)^{0.625}}],$$ where a constant positive parameter $A_Q$ is unique for all mesons with quantum numbers $Q=J^P$. Sets of mesons $J^P=0^-,~1^-,~0^+,~1^+,~2^+,~3^-$ and different flavors constituent quarks $(u=d,~s,~,c~,b)$ are considered.

hep-ph↗

arXiv2004

Masses of light mesons and analytical confinement

Spectrum of masses of light pseudoscalar ($π, K, η, η'$) and vector ($ρ, K^*, ω, ϕ$) mesons can be explained on the base of the following assumptions: (1) analytical confinement (propagators of quarks and gluons are entire analytical functions of the Gaussian type), (2) mesons are bound states of quark and gluons (the Bethe-Salpeter equation in the one-gluon exchange approximation) and (3) QCD coupling constant $α_s(M)$ is a monotone decreasing function of mass of a bound state $M$. The decay constants $f_π$ and $f_K$ are calculated.

hep-ph↗

arXiv2003

On The Ladder Bethe-Salpeter Equation

The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a scalar theory: two scalar fields (constituents) with mass $m$ interacting via an exchange of a scalar field (tieon) with mass $μ$. The BS equation is written in the form of an integral equation in the configuration Euclidean $x$-space with the kernel which for stable bound states $M<2m$ is a self-adjoint positive operator. The solution of the BS equation is formulated as a variational problem. The nonrelativistic limit of the BS equation is considered. The role of so-called abnormal states is discussed. The analytical form of test functions for which the accuracy of calculations of bound state masses is better than 1% (the comparison with available numerical calculations is done) is determined. These test functions make it possible to calculate analytically vertex functions describing the interaction of bound states with constituents. As a by-product a simple solution of the Wick-Cutkosky model for the case of massless bound states is demonstrated.

hep-ph↗

arXiv2002

Glueball as a bound state in the self-dual homogeneous gluon field

Using a simple relativistic QFT model of scalar fields we demonstrate that the analytic confinement (propagator is an entire function in the complex $p^2$--plane) and the weak coupling constant lead to the Regge behaviour of the two-particle bound states. In QCD we assume that the gluon vacuum is realized by the self-dual homogeneous classical field which is the solution of the Yang-Mills equations. This assumption leads to analytical confinement of quarks and gluons. We extract the colorless $0^{++}$ two-gluon state from the QCD generating functional in the one-gluon exchange approximation. The mass of this bound state is defined by the Bethe-Salpeter equation. The glueball mass is $1765~{\rm MeV}$ for $α_s=0.33$ if the gluon condensate is $<(α_s/π) G G >=0.012~{\rm GeV}^4$.

hep-ph↗

arXiv2002

Quartic Anharmonicity in Different Spatial Dimensions

A path-integral method effective beyond the perturbation expansion approach is suggested to consider the quartic anharmonicity in different spatial dimensions. Due to an optimal representation of the partition function, the leading term has already taken into account the correct strong-coupling behaviour. In the simplest cases of zero and one dimension we have obtained reasonable results in a simple way. Then, this technique is applied to the superrenormalizable scalar theory phi^4_2 in two dimensions. This results in an accurate estimation of the ground-state energy that provides exact weak- and strong-coupling behaviour already in the leading-order approximation. The next-to-leading terms give rise in insignificant corrections.

quant-ph↗

arXiv2001

Analytic Confinement and Regge Trajectories

A simple relativistic quantum field model with the Yukawa-type interaction is considered to demonstrate that the analytic confinement of the constituent ("quarks") and carrier ("gluons") particles explains qualitatively the basic dynamical properties of the spectrum of mesons considered as two-particle stable bound states of quarks and gluons: the quarks and gluons are confined, the glueballs represent bound states of massless gluons, the masses of mesons are larger than the sum of the constituent quark masses and the Regge trajectories of mesonic orbital excitations are almost linear.

hep-ph↗

arXiv2001

Solution of the radiative transfer equation in the separable approximation

A method for the fast and accurate solution of the radiative transfer equation in plane-parallel media with coherent isotropic scattering is presented. This largely analytical approach uses the formalism of meromorphic functions in order to obtain the total solution, i.e. the angle and depth variation of the radiation field. A discretization of space and angle coordinates is not required. For the further application in the accretion disks a particular case of a finite slab whose the midplane is the symmetry plane is considered.

astro-ph↗

arXiv2000

Glueball as a bound state in the selfdual homogeneous vacuum gluon field

Using a simple relativistic QFT model of scalar fields we demonstrate that the analytic confinement (propagator is an entire function in the complex p^2-plane) and the weak coupling constant lead to the Regge behaviour of the two-particle bound states. In QCD we assume that the gluon vacuum is realized by the selfdual homogeneous classical field which is the solution of the Yang-Mills equations. This assumption leads to analytical confinement of quarks and gluons. We extract the colorless 0(++) two-glouon state from the QCD generating functional in the one-gluon exchange approximation. The mass of this bound state is defined by the Bethe-Salpeter equation. The glueball mass varies in the region 1470{Mev} - 1600{Mev} for QCD coupling constant in the region 0.2 - 0.5 if the gluon condensate is 0.012 Gev^4.

hep-ph↗

arXiv1999

Bound states in quantum field theory, scalar fields

The main aim of this paper is to demonstrate the method called "the Bosonization of Nonlocal Currents" (BNC), used for calculations of bound states in a quark model, within the simplest relativistic quantum field model of two scalar fields with the Yukawa type interaction. A second aim is to clarify the relation between BNC and two widely used methods, employed in recent particle physics to calculate bound states of interacting particles, based on the nonrelativistic Schrodinger equation (the S-method), and the relativistic Bethe-Salpeter equation (the BS-method), and to determine the conditions on parameters of a quantum field model dictating a definite method to be applied. It is shown that all these methods can be applied only in the weak coupling regime when the effective dimensionless coupling constant should be less than 1. The basic parameter separating the relativistic and nonrelativistic pictures is the ratio of the masses of the exchange ("meson") and constituent ("nucleon") particles. If this ratio and the coupling constant are small then the potential picture takes place, i.e., the bound state is described by the nonrelativistic Schrodinger equation. Otherwise, the Bethe-Salpeter equation or the BNC should be employed. One notes that the BNC method has a slightly wider region of applicability in this case.

hep-ph↗

arXiv1998

(Anti-)self-dual homogeneous gluon field and axial anomaly in QCD

The transition form factor, decay width and charge form factor of pion are calculated within the model of induced nonlocal quark currents based on the assumption that the nonperturbative QCD vacuum can be characterized by a homogeneous (anti-)self-dual gluon field. It is shown that the interaction of the quark spin with the vacuum gluon field, being responsible in the model for the chiral symmetry breaking and the spectrum of light mesons, can also play the decisive role in forming the transition form factor and two-photon decay width. Asymptotic behavior of quark loops in the presence of the background gluon field for large momentum transfer is discussed.

hep-ph↗

arXiv1998

Confining Properties of the Homogeneous Self-Dual Field and the Effective Potential in SU(2) Yang-Mills Theory

We examine in non-Abelian gauge theory the heavy quark limit in the presence of the (anti-)self-dual homogeneous background field and see that a confining potential emerges, consistent with the Wilson criterion, although the potential is quadratic and not linear in the quark separation. This builds upon the well-known feature that propagators in such a background field are entire functions. The way in which deconfinement can occur at finite temperature is then studied in the static temporal gauge by calculation of the effective potential at high temperature. Finally we discuss the problems to be surmounted in setting up the calculation of the effective potential nonperturbatively on the lattice.

hep-th↗

arXiv1998

Self-dual homogeneous gluon field and electromagnetic structure of pion

hep-ph↗

arXiv1996

On bound states in quantum field theory

The mechanism of formation of bound states in the relativistic quantum field theory is demonstrated by the Yukawa field model. It is shown that the weak coupling regime leads to the potential picture, i.e. it is equivalent to the nonrelativistic limit in the bound state problem. In the strong coupling regime the potential picture is not valid and the method of bosonisation of fermion currents (so-called $Z_2=0$ method) should be used. Essentially the nonlocal fermion currents are found to be responsible for the origin of bound states and ultraviolet convergence of fermion loops.

hep-ph↗

arXiv1996

(Anti-)self-dual homogeneous vacuum gluon field as an origin of confinement and $SU_L(N_F)\times SU_R(N_F)$ symmetry breaking in QCD

It is shown that an (anti-)self-dual homogeneous vacuum gluon field appears in a natural way within the problem of calculation of the QCD partition function in the form of Euclidean functional integral with periodic boundary conditions. There is no violation of cluster property within this formulation, nor are parity, color and rotational symmetries broken explicitly. The massless limit of the product of the quark masses and condensates, $m_f \langle \barψ_f ψ_f \rangle$, is calculated to all loop orders. This quantity does not vanish and is proportional to the gluon condensate appearing due to the nonzero strength of the vacuum gluon field. We conclude that the gluon condensate can be considered as an order parameter both for confinement and chiral symmetry breaking.

hep-ph↗