Affiliation:
1. Mozyr State Pedagogical University named after I.P. Shamyakin
2. Brest State A. Pushkin University
3. B.I. Stepanov Institute of Physics of NAS of Belarus
4. Transilvania University of Brasov
Abstract
We start with the Stuckelberg tensor system of equations for a boson with spin states S = 1 and S = 0 and fixed intrinsic parity, which is transformed to the matrix form, then generalize this matrix system to the generally covariant case with the use of the tetrad method. This equation is detailed in spherical coordinates in the presence of an external Coulomb field. After separation of the variables we derive the system of 11 radial equations. By diagonalizing the space reflection operator, this system is splitted into two system of four and seven equations for the states with the parities P = (−1) j+1 and P = (−1) j respectively. The system for the states with the parities P = (−1) j+1 leads to the known solution and energy spectrum. The system of seven equations for the states with the parities P = (−1) j is solved for the states with the total angular momentum j = 0 in terms of hypergeometric functions. The system of seven equations for the states with the total angular momenta j = 1, 2, 3, ... turns out to be very complicated, the only nonrelativistic approximation has been studied. The derived nonrelativistic equations are solved in terms of confluent hypergeometric functions, and the corresponding energy spectra are found. In addition, the general form of the nonrelativistic equations for the the Stuckelberg particle is derived in the presence of an arbitrary electromagnetic field.
Publisher
Belarusian State University
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference20 articles.
1. E.C.G. Stueckelberg. Die Wechselwirkunskrafte in der Elektrodynamik und in der Feldtheorie der Kernkrafte (Teil II und III). Helv. Phys. Acta. 11, 299-312, 312-328 (1938).
2. V.M. Red'kov. On equations for the Dirak-Kahler field and bosons with different parities in the Riemannian space. Proceedings of the National Academy of Sciences of Belarus. Ser. fiz.-mat. 1, 90-95 (2000).
3. E. Ovsiyuk, O. Veko, V. Red'kov. Some consequences from the Dirac-Kahler theory: on intrinsic spinor sub-structure of the different boson wave functions. Nonlinear Phenomena in Complex Systems. 16, 13-23 (2013).
4. A.M. Ishkhanyan, O. Florea, E.M. Ovsiyuk, V.M. Red'kov. The Dirac-Kahler field in spherical Riemann space: boson interpretation, exact solutions. Proceedings of the Brest State Pedagogical University. Ser. Physics-Mathematics. 1, 15-26 (2015).
5. E.V. Ovsiyuk, A.N. Red'ko, V.M. Red'kov. The Dirac-Kahler particle in Lobachevsky space, nonrelativistic approximation, exact solutions. Proceedings of the National Academy of Sciences of Belarus. Ser. fiz.-mat. 4, 61-70 (2015).
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Massless Stueckelberg particle, solutions with cylindric symmetry;Proceedings of the Komi Science Centre of the Ural Division of the Russian Academy of Sciences;2023-09-21
2. Massless Stueckelberg field, exact solutions in Cartesian coordinates and gauge degrees of freedom;Proceedings of the Komi Science Centre of the Ural Division of the Russian Academy of Sciences;2023-09-21