Relativistic inverse scattering problem for a superposition of a nonlocal separable and a local quasipotential

Within the relativistic quasipotential approach to quantum field theory, the relativistic inverse scattering problem is solved for the case where the total quasipotential describing the interaction of two relativistic spinless particles having different masses is a superposition of a nonlocal separable and a local quasipotential. It is assumed that the local component of the total quasipotential is known and that there exist bound states in this local component. It is shown that the nonlocal separable component of the total interaction can be reconstructed provided that the local component, an increment of the phase shift, and the energies of bound states are known.     

Solving a relativistic quasipotential equation for a nonlocal separable interaction

Within the relativistic quasipotential approach to quantum field theory, a method is developed for solving a quasipotential equation for a nonlocal separable quasipotential simulating the interaction of two relativistic particles of unequal masses.     

Reconstructing a separable interaction within the relativistic quasipotential approach

Within the relativistic quasipotential approach to quantum field theory, a method is developed according to which a nonlocal separable quasipotential that represents the interaction between two relativistic particles of unequal masses can be reconstructed on the basis of the phase shift and bound-state energies.     

Form factor for a two-particle system within a relativistic quasipotential approach: Case of arbitrary masses and of a vector current

A new relativistic form factor for a bound two-particle system was obtained for the case of a vector current. The present consideration was performed within the relativistic quasipotential approach based on the covariant Hamiltonian formulation of quantum field theory by going over to the three-dimensional relativistic configuration representation for the case of interaction between two relativistic spinless particles of arbitrary mass.

     

Form factor of a relativistic two-particle system within the relativistic quasipotential approach: Case of an arbitrary masses and a scalar current

A new relativistic form factor for a bound two-particle system was obtained for the case of a scalar current. The respective analysis was performed within the relativistic quasipotential approach based on a covariant Hamiltonian formulation of quantum field theory by going over to a three-dimensional relativistic configuration representation for the case of the interaction of two relativistic spinless particles that have arbitrary masses.     

Accurate solutions of quasipotential equations with orbital momentum ℓ=1

It is shown that the integral quasipotential Logunov-Tavkhelidze and Kadyshevskii equations with local —in Lobachevskii momentum space — quasipotentials, the transforms of which are even rational functions of r in relativistic configurational space, may be reduced to a Sturm-Liouville problem in the case of unit orbital momentum. In the critical limit, when the bound-state mass is zero, accurate wave functions are obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 56–60, May, 1990.     

An application of the quasipotential method to pion nucleon scattering

The quasipotential method developed in Dubna Laboratory was applied to pion-nucleon scattering processes up to the energies 500 MeV, for obtaining the resonance behaviour of te P₃₃-phase shift. Although numerical calculations have not yet been completed, the existence of a resonance seems very probable.

     

Mass Spectrum of Mesons and Their Leptonic Decay Widths within the Relativistic Quasipotential Approach

New relativistic semiclassical conditions and leptonic decay widths are obtained within quantum chromodynamics for nonsingular confining quasipotentials and funnel-type potentials (instantoninteraction approximation). The respective analysis is performed within a fully covariant quasipotential approach in quantum field theory. This approach is formulated in the relativistic configuration representation for the case of interaction between two relativistic spinless particles of arbitrary mass.     

Threshold resummation <Emphasis Type="Italic">S</Emphasis> factor in QCD: The case of unequal masses

A new relativistic Coulomb-like threshold resummation S factor in quantum chromodynamics is obtained. The analysis in question is performed within the quantum-field-theory quasipotential approach formulated in the relativistic configuration representation for the case of interaction between two relativistic particles that have unequal masses.     

Bound-State Scalar Form Factor for Two Fermions within the Relativistic Quasipotential Approach

A new expression for the bound-state scalar form factor was obtained for two relativistic fermions of equal mass. The respective analysis was performed within the relativistic quasipotential approach based on the covariant Hamiltonian formulation of quantum field theory by means of the transition to the three-dimensional relativistic configuration representation for the interaction of two relativistic particles that have a spin of 1/2 and equal masses.     

Toward solving the problem of the nuclear-motion effect on the fine structure of the hydrogen-like atom by the quasipotential method

Coulomb interaction in the hydrogen-like atom is investigated by using the scattering amplitude free from singularities. The quasipotential method makes it possible to obtain new contributions to the fine shift of energy levels to the sixth order in the fine-structure constant.     

Quantum mechanical stability approach to the Coulomb quasipotential

The critical coupling constant characterizing the stability behaviour of the Coulomb quasipotential has been evaluated as α ? α_c = 2. The present stability approach is based on the quantum-mechanical controllability requirement of the dispersion shifts due to the interactions. The dispersions characterizing the Coulomb quasipotential have been established suitably within the high-energy euclidian region.     

Magnetic moment of a two-particle bound state in quantum electrodynamics

A quasipotential method for calculating relativistic and radiative corrections to the magnetic moment of a two-particle bound state is formulated for particles of arbitrary spin. It is shown that the expression for the g factors of bound particles involve O(α ²) terms depending on the particle spin. Numerical values are obtained for the g factors of the electron in the hydrogen atom and in deuterium.     

Quasipotential approach to the Coulomb bound state problem for spin-0 and spin-12 particles

A recently proposed local quasipotential equation is reviewed and applied to the electromagnetic interaction of a spin-0 and a $\text{spin}\text{-}\text{1}\text{2}$ particle. The Dirac particle is treated in a covariant two-component formalism in the neighbourhood of the mass shell. The fine structure of the bound state energy levels and the main part of the Lamb shift (of order α⁵ ln(1/α)) are evaluated with full account of relativistic recoil effects (without using any inverse mass expansion). Possible relevance of the techniques developed in this paper to fine structure calculations for meso-atomic systems is pointed out.     

Relativistic effects in the processes of heavy-quark fragmentation to double-heavy baryons

In the framework based on the quasipotential method and relativistic quark model, we investigate the heavy-quark fragmentation into double-heavy baryons with spin J = 1/2, 3/2. Adopting a two-step scenario for the fragmentation, we take into account relativistic corrections to the fragmentation probabilities at both stages of the production process for the double-heavy diquark and double-heavy baryon, correspondingly. We take into account all possible relativistic corrections including the terms connected with the transformation law of the bound-state wave function to the reference frame of the moving bound state. The text was submitted by the author in English.     

ΠN-scattering at high energies in the quasipotential approach

Experimental data on πN scattering in the momentum transfer region 0.01?|t|?1.0 (GeV/c)² and P_L?10 GeV/c are described in the framework of the quasipotential approach. The parameters of the quasipotential are found which allow the data to be described satisfactorily.     

The g factors of bound particles in quantum electrodynamics

A quasipotential method is formulated for calculating relativistic and radiative corrections to the magnetic moment of a two-particle bound state in the case of particles of arbitrary spin. It is shown that expressions for the g factors of bound particles contain terms of order O(α²) that depend on the spin of particles. Numerical values of the g factor of an electron in the hydrogen and deuterium atoms are obtained.     

Wave functions and mass spectrum for a system of two relativistic spinor quarks coupled by a chromodynamical interaction

Exact solutions of relativistic quasipotential equations in the configuration representation were found for a system of two spin-1/2 quarks interacting via a Coulomb-like chromodynamical potential. Quantization conditions were found for the pseudoscalar, pseudovector, and vector cases. The present analysis was performed within the Hamiltonian formulation of quantum field theory via a transition to the relativistic configuration representation for the case of two relativistic spin-1/2 quarks of equal mass.     

Relativistic dynamics on a null plane

In view of possible applications to the quark model and to hadron spectroscopy, we investigate relativistic Hamiltonian quantum theories of finitely many degrees of freedom. We make use of the fact that if null planes are used as initial surfaces, the structure of the theory closely resembles nonrelativistic quantum mechanics: the inner variables that describe the structure of the system uncouple from the motion of the system as a whole. The dynamical content of such a theory resides in the operators M, $\text{j}$ of mass and spin that act in the space carrying the inner degrees of freedom. Relativistic invariance is equivalent to the requirement that M and $\text{j}$ generate a unitary representation of U(2). In contrast to this requirement, the condition that the wavefunctions of the system transform covariantly strongly restricts the dynamics. It is proven that for systems containing two constituents, covariance is equivalent to an algebraic relation that involves M and $\text{j}$ — the angular condition. A class of solutions of the angular condition is provided by a particular type of local manifestly covariant wave equations. One nontrivial solution of this class, a relativistic oscillator is given in detail. Confinement models of this type represent an interesting alternative to the solutions of the angular condition that result from the perturbation expansion of a local field theory through the three-dimensional quasipotential versions of the Bethe-Salpeter equation.     

A covariant quasipotential operator for a composite system of two scaler particles

A quasipotential operator for a system of two scalar particles, and also an integral equation and a normalization condition for the wave function of the connected state, are obtained by the method of two-time Green's functions in an explicitly covariant form. The cases are considered of scalar and electromagnetic interactions of particles of the system.Frantsiska Skoriny Gomel' State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 112–118, June, 1993.