Nonlinear Phenomena in Complex Systems, 2021, Vol.24, No.4, pp.391-408

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2021, Vol.24, No.4, pp.391-408

Structure of the plane waves for a spin 3/2 particle, massive and massless cases, gauge symmetry

A.V. Ivashkevich

The structure of the plane waves solutions for a relativistic spin 3/2 particle described by 16-component vector-bispinor is studied. In massless case, two representations are used: Rarita – Schwinger basis, and a special second basis in which the wave equation contains the Levi-Civita tensor. In the second representation it becomes evident the existence of gauge solutions in the form of 4-gradient of an arbitrary bispinor. General solution of the massless equation consists of six independent components, it is proved in an explicit form that four of them may be identified with the gauge solutions, and therefore may be removed. This procedure is performed in the Rarita – Schwinger basis as well. For the massive case, in Rarita – Schwinger basis four independent solutions are constructed explicitly.

Key words: spin 3/2, Rarita and Schwinger equation, plane waves, linearly independent solutions, massive and massless particles, exclusion of gauge degrees of freedom

DOI: https://doi.org/10.33581/1561-4085-2021-24-4-391-408

Full text: Acrobat PDF (429 KB)