Relativistic Configuration Representation Research Articles

Approximate analytic solution of the Logunov–Tavkhelidze equation for a one-dimensional oscillator potential in the relativistic configuration representation

Approximate analytic solution of the Logunov–Tavkhelidze equation for a one-dimensional oscillator potential in the relativistic configuration representation

Приближенное аналитическое решение уравнения Логунова-Тавхелидзе для одномерного осцилляторного потенциала в релятивистском конфигурационном представлении

Найдены приближенные аналитические решения уравнения Логунова-Тавхелидзе в случае потенциала, который в одномерном релятивистском конфигурационном представлении имеет вид, аналогичный потенциалу нерелятивистского гармонического осциллятора в координатном представлении. Волновые функции получены в импульсном и в релятивистском конфигурационном представлениях. Приближенные значения энергии релятивистского гармонического осциллятора являются корнями трансцендентных уравнений. Волновые функции в релятивистском конфигурационном представлении имеют дополнительные нули по сравнению с волновыми функциями соответствующих состояний нерелятивистского гармонического осциллятора в координатном представлении.

On Threshold Resummation S-Factor for a System of Two Relativistic Spinor Particles with Arbitrary Masses

We present a new threshold resummation S-factor obtained for a composite system of two relativistic spin 1/2 particles of arbitrary masses interacting via a Coulomb-like chromodynamical potential. The analysis is performed in the framework of a relativistic quasipotential approach in the Hamiltonian formulation of the quantum field theory in the relativistic configuration representation. The pseudoscalar, vector, and pseudovector systems are considered. The difference in the behavior of the S-factor for these cases is discussed. A connection between the new and the previously obtained S-factors for spinless particles of arbitrary masses and relativistic spinor particles of equal masses is established.

Semiclassical Quantization Condition for a Relativistic Bound System of Two Equal-Mass Fermions

New relativistic semiclassical quantization conditions are obtained for a system of two equal-mass fermions interacting via nonsingular confining quasipotentials and quasipotentials of the funnel type. The quantization conditions are specified in the pseudoscalar, pseudovector, and vector cases. The respective analysis is performed within the Hamiltonian formulation of quantum field theory via a transition to the relativistic configuration representation for the case of a bound system formed by two relativistic spin particles of equal mass.

Form Factor for a Two-Fermion Composite System: Case of Equal Masses and Vector Current

New expressions for components of the form factor for a composite system of two equal-mass relativistic fermions were obtained for the vector-current case. The respective consideration was performed within the relativistic quasipotential approach based on the covariant Hamiltonian formulation of quantum field theory via a transition to the three-dimensional relativistic configuration representation for the case of interaction between two equal-mass particles of spin 1/2.

Threshold Resummation S-Factor for a System of Two Relativistic Spinor Quarks

A new threshold resummation S-factor in quantum chromodynamics is obtained for a composite system of two relativistic spin-1/2 quarks having identical masses and interacting via a Coulomb-like chromodynamical potential. The pseudoscalar, vector, and pseudovector cases are considered. The present analysis is performed on the basis of the relativistic quasipotential approach in the Hamiltonian formulation of quantum field theory via a transition to the relativistic configuration representation for the case of a composite system formed by two relativistic particles of equal mass.

Solution of the Logunov–Tavkhelidze Equation for the Three-Dimensional Oscillator Potential in the Relativistic Configuration Representation

Approximate analytical and numerical solutions of the three-dimensional Logunov–Tavkhelidze equation are found for the spherically symmetric case. Solutions are obtained in momentum and relativistic configuration representations. The wave functions in the relativistic configuration representation have additional zeroes compared to the wave functions of the nonrelativistic harmonic oscillator in the coordinate representation.

Solution of Partial Quasipotential Equations in the Relativistic Configuration Representation

Within the framework of the quasipotential approach, some variants of the interaction of two relativistic spinless particles are considered in the relativistic configuration representation. Numerical solutions of the problem of bound states and scattering states of two-particle systems with zero and nonzero orbital angular momentum are presented. The coupling between resonance and bound states is investigated. A comparison of the results with the nonrelativistic case is provided.

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.

Partial Quasipotential Equations in the Relativistic Configuration Representation

Quasispotential equations for the scattering states of two relativistic particles are considered. A representation of the relativistic partial waves in terms of the associated Legendre functions with integer subscript and hyperbolic cotangent of the rapidity as their argument is found. An explicit form of the partial Green’s functions is found in the relativistic configuration representation for three versions of the quasipotential equations. An algorithm for numerical solution of the partial equations for scattering states of the particles with nonzero orbital angular momentum is presented.

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.

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.

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.

Numerical solution of relativistic problems on bound states of systems of two spinless particles

Numerical solutions of the equations of quantum field theory describing bound s-states of systems of two scalar particles have been found for the following three cases: a one-boson exchange potential, a superposition of such potentials, and also the Coulomb potential in the relativistic configuration representation. On the basis of these solutions, the elastic scattering form factors and decay constants for decay of a two-particle system into two photons have been obtained. It is shown that the number of zeros of the elastic form factors coincides with the number of zeros of the wave functions and is equal to the quantum number of the state of the system minus one. The obtained energy spectra and decay constants are compared with the experimentally measured values for positronium.

The resummation L-factor in the relativistic quasipotential approach

We obtain a new relativistic Coulomb-like resummation factor (L-factor) for an arbitrary orbital moment l ≥ 0. We work within the fully covariant quasipotential approach in quantum field theory formulated in the relativistic configuration representation in the case of two interacting relativistic particles with arbitrary masses.

Threshold resummation S factor in QCD: The case of unequal masses

The new relativistic Coulomb-like threshold resummation $S$-factor in quantum chromodynamics is obtained. The consideration is given within the framework of quasipotential approach in quantum field theory which is formulated in relativistic configuration representation for two particles of unequal masses.

Covariant two-particle wave functions for model quasipotentials that admit exact solutions. II. Solutions in the relativistic configuration representation

Covariant two-particle wave functions for model quasipotentials that admit exact solutions. II. Solutions in the relativistic configuration representation