Covariant equations and resonance states of two-particle systems with $\delta$-function potentials
Problemy fiziki, matematiki i tehniki, no. 1 (2015), pp. 11-15.

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

The complex resonance energy (rapidity) spectra of relativistic two particle systems are found on the basis of exact solutions of the covariant two-particle equations with $\delta$-function potential and a superposition of two $\delta$-function potentials. It is established that the exact partial two particle relativistic amplitudes have resonance behavior precisely at those energy (rapidity) values, which correspond to the real part of the complex resonance energies.
Keywords: relativistic two-particle equations, relativistic configuration representation, $\delta$-function potential, resonance state, scattering amplitude, scattering cross section.
@article{PFMT_2015_1_a1,
     author = {V. N. Kapshai and M. S. Danilchenko and Yu. A. Grishechkin},
     title = {Covariant equations and resonance states of two-particle systems with $\delta$-function potentials},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {11--15},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2015_1_a1/}
}
TY  - JOUR
AU  - V. N. Kapshai
AU  - M. S. Danilchenko
AU  - Yu. A. Grishechkin
TI  - Covariant equations and resonance states of two-particle systems with $\delta$-function potentials
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2015
SP  - 11
EP  - 15
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2015_1_a1/
LA  - ru
ID  - PFMT_2015_1_a1
ER  - 
%0 Journal Article
%A V. N. Kapshai
%A M. S. Danilchenko
%A Yu. A. Grishechkin
%T Covariant equations and resonance states of two-particle systems with $\delta$-function potentials
%J Problemy fiziki, matematiki i tehniki
%D 2015
%P 11-15
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2015_1_a1/
%G ru
%F PFMT_2015_1_a1
V. N. Kapshai; M. S. Danilchenko; Yu. A. Grishechkin. Covariant equations and resonance states of two-particle systems with $\delta$-function potentials. Problemy fiziki, matematiki i tehniki, no. 1 (2015), pp. 11-15. http://geodesic.mathdoc.fr/item/PFMT_2015_1_a1/

[1] V. N. Kapshai, T. A. Alferova, “Relativistic two-particle one-dimensional scattering problem for superposition of $\delta$-potentials”, J. Phys. A, 32 (1999), 5329–5342 | DOI

[2] V. N. Kapshai, T. A. Alferova, “Odnomernye relyativistskie zadachi o svyazannykh sostoyaniyakh i rasseyanii dlya superpozitsii kvazipotentsialov nulevogo radiusa”, Izv. Vuzov. Fizika, 2002, no. 1, 3–10

[3] A. A. Logunov, A. N. Tavkhelidze, “Quasi-Optical Approach in Quantum Field Theory”, Nuovo Cimento, 29:2 (1963), 380–399 | DOI

[4] V. G. Kadyshevsky, “Quasipotential type equation for the relativistic scattering amplitude”, Nucl. Phys. B, 6:1 (1968), 125–148 | DOI

[5] V. G. Kadyshevskii, R. M. Mir-Kasimov, N. B. Skachkov, “Trekhmernaya formulirovka relyativistskoi problemy dvukh tel”, EChAYa, 2:3 (1972), 635–690

[6] V. Kapshai, Yu. Grishechkin, Relativistic two-particle equations with superposition of delta-shell potentials: scattering and bound states, 2013, arXiv: (Date of access: 06.12.2013) 1312.1902[math-ph]

[7] 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, Proced. of the Sixth Annual Seminar NPCS'97, Academy of Sciences of Belarus. Inst. of Phys., Minsk, 1998, 78–85

[8] V. N. Kapshai, K. P. Shilyaeva, Yu. A. Grishechkin, “Rezonansnye sostoyaniya sostavnykh sistem i kovariantnye dvukhchastichnye uravneniya teorii polya”, Kovariantnye metody v teoreticheskoi fizike. Fizika elementarnykh chastits i teoriya otnositelnosti, Sb. nauchnykh trudov, Institut fiziki im. B. I. Stepanova Natsionalnoi Akademii Nauk Belarusi, Minsk, 2011, 79–88

[9] Dzh. Teilor, Teoriya rasseyaniya, Mir, M., 1975, 568 pp.

[10] R. Nyuton, Teoriya rasseyaniya voln i chastits, Mir, M., 1969, 608 pp.