Affiliation:
1. B.I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus
2. Mozyr State Pedagogical University named after I. P. Shamyakin
3. B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus
Abstract
In the present paper, the system of 11 equations for massive
Stueckelberg particle is studied in presence of the external
uniform electric field. We apply covariant formalism according
to the general tetrad approach by Tetrode-Weyl-Fock-Ivanenko
specified for cylindrical coordinates. After separating
the variables, we derive the system of the first-order differential
equations in partial derivatives with respect to coordinates
(r, z). To resolve this system, we apply the Fedorov-
Gronskiy method, thereby we consider the 11-dimensional
spin operator and find on this base three projective operators,
which permit us to expand the complete wave function
in the sum of three parts. Besides, according to the general
method, dependence of each projective constituent on the
variable r should be determined by only one function. Also, in
accordance with the general method we impose the first-order
constraints which permit us to transform all differential
equations in partial derivatives with respect to coordinates
(r, z) into the system of 11 first-order ordinary differential
equations in the variable z. The last system is solved in terms
of confluent hypergeometric functions. In total, four independent
types of solutions have been constructed, in contrast to
the case of the ordinary spin 1 particle described by Daffin-
Kemmer equation when only three types of solutions are possible.
Reference8 articles.
1. Stueckelberg, E. C. G. Die Wechselwirkungskräfte in der Elektrodynamik und in der Feldtheorie der Kernkräfte (Teil II und III) / E. C. G. Stueckelberg // Helv. Phys. Acta. – 1938. – Vol. 11. – P. 299–312. – P. 312–328., Stueckelberg, E. C. G. Die Wechselwirkungskräfte in der Elektrodynamik und in der Feldtheorie der Kernkräfte (Teil II und III) / E. C. G. Stueckelberg // Helv. Phys. Acta. – 1938. – Vol. 11. – P. 299–312. – P. 312–328.
2. Ruegg, H. The Stueckelberg field / H. Ruegg, M. Ruiz- Altabal // Int. J. Mod. Phys. A. – 2004. – Vol. 119. – P. 3265–3348., Ruegg, H. The Stueckelberg field / H. Ruegg, M. Ruiz- Altabal // Int. J. Mod. Phys. A. – 2004. – Vol. 119. – P. 3265–3348.
3. Овсиюк, E. M. Частица Штюкельберга во внешнем магнитном поле. Метод проективных операторов / E. M. Овсиюк, А. П. Сафронов, А. В. Ивашкевич, О. А. Семенюк // Известия Коми научного центра Уральского отделения Российской академии наук. Серия «Физико-математические науки». – 2022. – № 5 (57). –С. 69–78., Ovsiyuk, E. M. Chastisa Shtukelberga vo vneshnem magnitnom pole. Metod proektivnih operatorov [Stuckelberg particle in external magnetic field, and the method of projective operators] / E. M. Ovsiyuk [et al.] // Proceedings of the Komi Science Centre of the Ural Branch of the Russian Academy of Sciences. Series “Physical and Mathematical Sciences”. – 2022. – № 5 (57). – P. 69–78.
4. Овсиюк, E. M. Частица Штюкельберга во внешнем магнитном поле. Нерелятивистское приближение. Точные решения / E. M. Овсиюк, А. П. Сафронов, А. В. Ивашкевич, О. А. Семенюк // Известия Коми научного центра Уральского отделения Российской академии наук. Серия «Физико-математические науки». – 2022. –№ 5 (57). – С. 79–88., Ovsiyuk, E. M. Stueckelberg particle in external magnetic field. Nonrelativistic approximation. Exact solutions / E. M. Ovsiyuk, A. P. Safronov, A. V. Ivashkevich, O. A. Semenyuk // Proceedings of the Komi Science Centre of the Ural Branch of the Russian Academy of Sciences. Series “Physical and Mathematical Sciences”. – 2022. – № 5 (57). – P. 79–88.
5. Ovsiyuk, E. M. Stuckelberg particle in the Coulomb field, non-relativistic approximation, wave functions and spectra / E. M. Ovsiyuk [et al.] // Nonlinear Phenomena in Complex Systems. – 2022. – Vol. 25, № 4. – P. 387–404., Ovsiyuk, E. M. Stuckelberg particle in the Coulomb field, non-relativistic approximation, wave functions and spectra / E. M. Ovsiyuk [et al.] // Nonlinear Phenomena in Complex Systems. – 2022. – Vol. 25, № 4. – P. 387–404.