Spin 3/2 particle: Fradkin theory, nonrelativistic approximation
https://doi.org/10.29235/1561-2430-2021-57-3-353-373
Abstract
The well-known relativistic wave equation for a spin 3/2 particle proposed by Pauli and Fierz is based on the use of the wave function with the transformation properties of vector-bispinor. Less known is the Fradkin theory based on the vector-bispinor wave function as well. At the vanishing Fradkin parameter Λ, this equation reduces to the Pauli – Fierz equation. To clarify the physical meaning of the additional parameter, in the present paper the nonrelativistic approximation in the Fradkin equation is studied, at this we take into account the presence of external electromagnetic fields. With the use of the technique of projective operators, we decompose the wave function into big and small constituents, and then derive a generalized nonrelativistic equation for a 16-component wave function. It is shown that when preserving only the terms of first order in the Fradkin parameter Λ after transition to 4 independent components of the nonrelativistic wave function there arises the ordinary nonrelativistic equation for the Pauli – Fierz theory without any additional interaction with electromagnetic fields. When preserving the terms of second order in parameter Λ, we obtain a 4-component nonrelativistic equation with additional interaction; however, only with the magnetic field. This interaction is quadratic in magnetic field components and governed by six 4-dimensional matrices. So the Fradkin theory may be understood as relevant to a particle with magnetic quadrupole moment.
Keywords
spin 3/2,
Pauli – Fierz theory,
Fradkin theory,
projective operators,
nonrelativistic approximation,
magnetic quadrupole moment
Supporting agencies: The research was carried out under the financial support of the Belarusian Republican Foundation for Fundamental Research (grant no. Ф20-РА-007).
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 – Undergraduate
68-2, Nezavisimosti Ave., 220072, Minsk
O. A. Vasiluyk
Brest State University named after A. S. Pushkin
Belarus
Belarus
Olga A. Vasiluyk – Teacher
21, boulevard Kosmonavtov, 224016, Brest
E. M. Ovsiyuk
Mozyr State Pedagogical University named after I. P. Shamyakin
Belarus
Belarus
Еlena М. Оvsiyuk – Ph. D. (Physics and Mathematics), Associate 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), Associate Professor, Associate 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
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