Three-Dimensional Formulation of the Relativistic Two-Body Problem

Кадышевский, Владимир Георгиевич; Mir‐Kasimov, R. M.; Skachkov, N. B.

doi:10.1007/978-1-4684-7550-0_3

Cited by 15 publications

(23 citation statements)

References 17 publications

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“…Independently, this idea was developed by A. P. Kotelnikov from the university in Kazan, where N. Lobachevski worked out his geometry [20]. In the scope of the quantum relativistic dynamics the hyperbolic geometry intensively was exploited in, so-called, quasipotential models (see, for instance, [21], [22]). Two-and three-dimensional Euclidean geometries are unique what allow geometric observations.…”

Section: Discussionmentioning

confidence: 99%

Geometrical Interpretation of General Complex Algebra and its Application in Relativistic Mechanics

Yamaleev

2007

AACA

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In a generalized formulation of the relativistic dynamics with internal conformation an important role is played by a quadratic polynomial, the coefficients and eigenvalues of which are generated by outer and inner momenta of the relativistic particle. This polynomial induces the general complex algebra, GC. In this paper we explore the geometrical and physical aspects of the evolution generated by the algebraic operations of the GC-algebra. It is shown that the geometrical image of the GC-number is given by a straight line passing through two given points in an euclidean plane. In this representation the straight line is characterized by a norm and an argument. The motions of the straight line are described by hyperbolic trigonometry which brings a correspondence between the Euclidean geometry and the hyperbolic one. It is proved that the evolution equation governed by the generator of the GC-algebra describes the energy conservation law of the relativistic particle. This evolution is depicted on the Euclidean plane as a rotational motion of the straight line, tangent to the circle with radius equal to the mass of the particle. In this way we come to new representation for the momenta in relativistic dynamics.

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Section: Discussionmentioning

confidence: 99%

Geometrical Interpretation of General Complex Algebra and its Application in Relativistic Mechanics

Yamaleev

2007

AACA

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“…In this case, the matrix element of transition from one space to another is the Shapiro function rather than the plane wave [3]. Analogous problem was solved by Kadyshevskii et al [4] who constructed a relativistic configuration space. The same situation arises when implementing the Wigner function formalism in the Lobachevskii curved space [5].…”

Section: Introductionmentioning

confidence: 97%

Description of spatial characteristics of elastic processes within the formalism of the Wigner functions

et al. 2011

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Definition of the Wigner function is given and its application to a description of elastic scattering processes is analyzed. A new element of the well-known formalism is a choice of the phase space in which the Wigner function is assigned as a quasi-probability distribution. This is a 4-dimensional space of canonically conjugated quantities -transverse momentum of the scattered particle and the projection of the closest particle approach vector onto the plane perpendicular to the incident particle momentum. Exact expression for the average squared radius of the region of scattered particle production through the scattering amplitude is presented.

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“…In the present study, an expression for the elastic form factor for a bound relativistic two-particle system is obtained for the case of a vector current by using the relativistic quasipotential (RQP) approach based on the Hamiltonian formulation of quantum field theory [8,9] and by going over to the relativistic configuration representation for interaction between two relativistic spinless particles with arbitrary masses m 1 and m 2 [20,21].…”

Section: Introductionmentioning

confidence: 99%

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

Chernichenko

2015

Phys. Atom. Nuclei

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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 threedimensional relativistic configuration representation for the case of interaction between two relativistic spinless particles of arbitrary mass.

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Three-Dimensional Formulation of the Relativistic Two-Body Problem

Cited by 15 publications

References 17 publications

Geometrical Interpretation of General Complex Algebra and its Application in Relativistic Mechanics

Geometrical Interpretation of General Complex Algebra and its Application in Relativistic Mechanics

Description of spatial characteristics of elastic processes within the formalism of the Wigner functions

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

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