Spin 3/2 particle: Puali – Fierz theory, non-relativistic approximation
https://doi.org/10.29235/1561-2430-2020-56-3-335-349
Abstract
The relativistic wave equation is well-known for a spin 3/2 particle proposed by W. E. Pauli and M. E. Fierz and based on the 16-component wave function with the transformation properties of the vector-bispinor. In this paper, we investigated the nonrelativistic approximation in this theory. Starting with the first-order equation formalism and representation of Pauli – Fierz equation in the Petras basis, also applying the method of generalized Kronecker symbols and elements of the complete matrix algebras, and decomposing the wave function into large and small nonrelativistic constituents with the help of projective operators, we have derived a Pauli-like equation for the 4-component wave function describing the non-relativistic particle with a 3/2 spin.
About the Authors
A. V. Ivashkevich
B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus
Belarus
Belarus
Alina V. Ivashkevich – Master Student
68-2, Nezavisimosti Ave., 220072, Minsk
Ya. A. Voynova
Minsk Suvorov Military School
Belarus
Belarus
Yanina A. Voynova – Ph. D. (Physics and Mathematics), Teacher
29, M. Bogdanovich Str., 220029, Minsk
E. M. Оvsiyuk
Mozyr State Pedagogical University named after I. P. Shamyakin
Belarus
Belarus
Еlena М. Оvsiyuk – Ph. D. (Physics and Mathematics), Assistant Professor, Head of the Department of Theoretical Physics and Applied Informatics
28, Studencheskaya Str., 247760, Mozyr
V. V. Kisel
Belarusian State University of Informatics and Radioelectronics
Belarus
Belarus
Vasily V. Kisel – Ph. D. (Physics and Mathematics), Assistant Professor, Assistant Professor of the Department of Physics
6, P. Brovka Str., 220013, Minsk
V. M. Red’kov
B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus
Belarus
Belarus
Viktor M. Red’kov – Dr. Sc. (Physics and Mathematics), Chief Researcher of the Center «Fundamental Interactions and Astrophysics»
68-2, Nezavisimosti Ave., 220072, Minsk
References
1. Dirac P. A. M. Relativistic wave equations. Proceedings of the Royal Society of London. Series A – Mathematical and Physical Sciences, 1936, vol. 155, no. 886, pp. 447–459. https://doi.org/10.1098/rspa.1936.0111
2. Majorana E. Teoria simmetrica dell’elettrone e del positrone. Nuovo Cimento, 1937, vol. 14, no. 4, pp. 171–186. https://doi.org/10.1007/bf02961314
3. Fierz M. Über die relativistische theorie KraftefreierTeilchen mit beliebigem Spin. Helvetica Physica Acta, 1939, vol. 12, pp. 3–37.
4. Pauli W. Über relativistische Feldleichungen von Teilchen mit beliebigem Spin im elektromagnetishen Feld. Helvetica Physica Acta, 1939, vol. 12, pp. 297–300.
5. Rarita W., Schwinger J. S. On a theory of particles with half-integral spin. Physical Review, 1941, vol. 60, no. 1, pp. 61–64. https://doi.org/10.1103/physrev.60.61
6. Bhabha H. J. Relativistic wave equations for the elementary particles. Reviews of Modern Physics, 1945, vol. 17, no. 2–3, pp. 200–216. https://doi.org/10.1103/revmodphys.17.200
7. Gelfand I. M., Yaglom A. M. General relativistically invariant equations and infinite-dimensional representations of the Lorentz group. Zhurnal Eksperimentalnoy i Teoreticheskoy Fiziki = Journal of Experimental and Theoretical Physics, 1948, vol. 18, no. 8, pp. 703–733 (in Russian).
8. Fradkin E. S. To the theory of particles with higher spins. Zhurnal Eksperimentalnoy i Teoreticheskoy Fiziki = Journal of Experimental and Theoretical Physics, 1950, vol. 20, no. 1, pp. 27–38 (in Russian).
9. Fedorov F. I. Generalized relativistic wave equations. Doklady Akademii nauk SSSR = Proceedings of the Academy of Sciences of the USSR, 1952, vol. 82, no. 1, pp. 37–40 (in Russian).
10. Feinberg V. Ya. On the theory of interaction of particles with higher spins with electromagnetic and meson fields. Trudy Fizicheskogo instituta im. P. N. Lebedeva Akademii nauk SSSR = Proceedings of the Lebedev Physics Institute of the Academy of Sciences of the USSR, 1955, vol. 6, pp. 269–332 (in Russian).
11. Petras M. A note to Bhabha’s equation for a particle with maximum spin 3/2. Czechoslovak Journal of Physics, 1955, vol. 5, no. 3, pp. 418–419.
12. Bogush A. A. Equation for a 3/2 particle with anomalous magnetic moment. Izvestiya vysshih uchebnyh zavedenij. Fizika = Russian Physics Journal, 1984, vol. 1, pp. 23–27 (in Russian).
13. Pletyukhov V. A., Strazhev V. I. To the theory of particles of spin 3/2. Izvestiya vysshih uchebnyh zavedenij. Fizika = Russian Physics Journal, 1985, vol. 28, no. 1, pp. 91–95 (in Russian).
14. Pletyukhov V. A., Strazhev V. I. On the relationship between various formulations of particle theory with spin 3/2. Vestsі Akademіі navuk Belarusі BSSR. Seryia fіzіka-matematychnykh navuk = Proceedings of the Academy of Sciences of the BSSR. Physics and Mathematics series, 1985, vol. 5, pp. 90–95 (in Russian).
15. Red’kov V. M. Particle fields in the Riemann space and the Lorents group. Minsk, Belaruskaya navuka Publ., 2009. 486 p. (in Russian).
16. Pletyukhov V. A., Red’kov V. M., Strazhev V. I. Relativistic wave equations and internal degrees of freedom. Minsk, Belaruskaya navuka Publ., 2015. 328 p. (in Russian).
17. Kisel V. V., Ovsiyuk E. M., Veko O. V., Voynova Ya. A., Balan V., Red’kov V. M. Elementary particles with internal structure in external fields. I. General theory, II. Physical problems. New York, Nova Science Publishers Inc., 2018. 404 p.
18. Kisel V. V., Ovsiyuk E. М., Ivashkevich A. V., Red’kov V. M. Fradkin equation for a spin 3/2 particle in presence of external electromagnetic and gravitational fields. Ukraine Journal of Physics, 2019, vol. 64, no. 12, pp. 1112–1117. https://doi.org/10.15407/ujpe64.12.1112
Review
Views: 1307
Email this article 