Resonance states of relativistic systems and covariant two-particle equations
Problemy fiziki, matematiki i tehniki, no. 4 (2011), pp. 33-37.

Voir la notice de l'article provenant de la source Math-Net.Ru

Method for determination of resonance states of the relativistic two-particle system and analysis of their influence on the cross section is presented. The method is based on the integral equations in the relativistic configurational representation. This method is applied for the identification of the scattering cross sections structures for a model potential.
Keywords: two-particle integral equations, relativistic configurational representation, complex scaling, resonance states, scattering amplitude, cross section.
@article{PFMT_2011_4_a6,
     author = {V. N. Kapshai and K. P. Shilyaeva and Yu. A. Grishechkin},
     title = {Resonance states of relativistic systems and covariant two-particle equations},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {33--37},
     publisher = {mathdoc},
     number = {4},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2011_4_a6/}
}
TY  - JOUR
AU  - V. N. Kapshai
AU  - K. P. Shilyaeva
AU  - Yu. A. Grishechkin
TI  - Resonance states of relativistic systems and covariant two-particle equations
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2011
SP  - 33
EP  - 37
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2011_4_a6/
LA  - en
ID  - PFMT_2011_4_a6
ER  - 
%0 Journal Article
%A V. N. Kapshai
%A K. P. Shilyaeva
%A Yu. A. Grishechkin
%T Resonance states of relativistic systems and covariant two-particle equations
%J Problemy fiziki, matematiki i tehniki
%D 2011
%P 33-37
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2011_4_a6/
%G en
%F PFMT_2011_4_a6
V. N. Kapshai; K. P. Shilyaeva; Yu. A. Grishechkin. Resonance states of relativistic systems and covariant two-particle equations. Problemy fiziki, matematiki i tehniki, no. 4 (2011), pp. 33-37. http://geodesic.mathdoc.fr/item/PFMT_2011_4_a6/

[1] A. A. Logunov, A. N. Tavkhelidze, “Quasi-Optical Approach in Quantum Field Theory”, Nuovo Cimento, 29 (1963), 380–399 | DOI | MR

[2] V. G. Kadyshevsky, “Quasipotential type equation for the relativistic scattering amplitude”, Nucl. Phys. B, 6 (1968), 125–148 | DOI

[3] V. G. Kadyshevsky, R. M. Mir-Kasimov, N. B. Skachkov, “Quasipotential approach and the expansion in relativistic spherical functions”, Nuovo Cimento A, 55 (1968), 233–257 | DOI

[4] V. G. Kadyshevskii, R. M. Mir-Kasimov, N. B. Skachkov, “Trekhmernaya formulirovka relyativistskoi problemy dvukh tel”, EChAYa, 2 (1972), 635–690

[5] I. S. Shapiro, “Razlozhenie funktsii po neprivodimym predstavleniyam gruppy Lorentsa”, Dokl. AN SSSR, 106 (1956), 647–649 | Zbl

[6] T. A. Alferova, V. N. Kapshai, “Expansion in terms of matrix elements of the Lorentz group unitary irreducible representations and integral equations for scattering states relativistic wave functions”, Nonlinear phenomena in complex systems, Proceed. of the Sixth Annual Seminar NPCS'97, Academy of Sciences of Belarus. Inst. of Phys., Minsk, 1998, 78–85

[7] R. J. Taylor, Scattering theory, John Wiley Sons, New York–London–Sydney–Toronto, 1972, 570 pp.

[8] J. Nuttal, H. L. Cohen, “Method of Complex Coordinates for Three-Body Calculations above the Breakup Threshold”, Phys. Rev., 188 (1969), 1542–1544 | DOI

[9] E. Balslev, J. M. Combes, “Spectral properties of many body Schrödinger operators with dilation-analytic interactions”, Commun. Math. Phys., 22 (1971), 280–294 | DOI | MR | Zbl

[10] K. Shilyaeva, N. Elander, E. Yarevsky, “Role of Resonances in Building Cross Sections: Comparison Between the Mittag–Leffler and the T-matrix Green Function Expansion Approaches”, Int. J. Quantum Chem., 107 (2007), 1301–1305 | DOI

[11] G. Arfken, Mathematical Methods for Physicists, Academic Press, San Diego, 1985, 985 pp. | MR

[12] A. Abrashkevich, I. V. Puzynin, “CANM, a program for numerical solution of a system of nlinear equations using the continuous analog of Newton's method”, Comput. Phys. Commun., 156 (2004), 154–170 | DOI | Zbl