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Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series

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Spin 3/2 particle: Puali – Fierz and Fradkin models, interaction with external fields

https://doi.org/10.29235/1561-2430-2020-56-3-350-360

Abstract

In the frame of the general Gel’fand – Yaglom formalism, the Fradkin theory for a spin 3/2 particle in presence of external fields is investigated. Applying the standard requirements of relativistic invariance, P-symmetry, existence of a Lagrangian for the model, we derive a set of spinor equations, first in absence of external fields. The wave function consists of a bispinor and a vector-bispinor. It is shown that in absence of external fields the Fradkin model is reduced to the Pauli – Fierz theory. Taking into account the presence of external electromagnetic fields, the Fradkin theory can be turned to the minimal form of the equation for the main bispinor. This equation contains an additional interaction term governed by the electromagnetic tensor Fαβ. Meanwhile, there appears a parameter in the Fradkin equation related to any characteristic of the particle additional to its charge. The theory is generalized for taking into account the pseudo-Riemannian space-time geometry. In this case, the Fradkin equation contains an additional interaction term, governed by the Ricci tensor Rαβ. If the electric charge of the particle is zero, the Fradkin model remains correct and describes a neutral spin 3/2 particle of the Majorana type interacting nonminimally with the geometrical background through the Ricci tensor. To clarify the meaning of the additional physical characteristics underlying the Fradkin model in contrast to the Pauli – Fierz one we have considered nonrelativistic approximation for both theories in presence of an external uniform magnetic field, and found respective energy spectra. The structure of the ninrelativistic Fradkin equation permits to consider such an additional parameter as polarizability.

About the Authors

A. V. Ivashkevich
B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus
Belarus

Alina V. Ivashkevich – Master Student

68-2, Nezavisimosti Ave., 220072, Minsk



Ya. A. Voynova
Minsk Suvorov Military School
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

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

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

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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