Beltrami-Moses spinors in electromagnetism (Q1842502)

The electromagnetic field can be described by a second rank spinor (which means a \(2 \times 2\) complex matrix) and, due to this, all Maxwell equations can be written in a single formula. This observation is quite old -- some references to earlier works were given by \textit{W. E. Baylis} [Special relativity with \(2 \times 2\) matrices, Am. J. Phys. 48, 918 (1980)]. Beltrami-Moses vectors are eigenfunctions of the curl operator (because of nonclear reasons, curl denoted as \(\nabla \wedge\), not \(\nabla \times)\). The author translates those functions into the matrix language and calls them Beltrami-Moses spinors. Since they are specific exponential functions, a kind of integral representation (of a general electromagnetic field) has been introduced and named Beltrami-Moses transform. It is a modification of the Fourier transformation. As an application, counterparts of surface harmonics are given, expressed in terms of Bessel functions. Second rank spinors are representations of \(Cl_3\), the Clifford algebra of three-dimensional Euclidean space, so the same quantities and equations of classical electrodynamics can be represented in \(Cl_3\) without resort to any matrices, see e.g. \textit{D. Hestenes} [Space-time algebra, Gordon and Breach, New York (1966; Zbl 0183.289)]. Baylis recognized this fact as can be noticed from his later joint paper with \textit{G. Jones} [J. Phys. A, Math. Gen. 22, No. 1, 17-29 (1989; Zbl 0667.15026)] written completely in terms of \(Cl_3\). These references are not mentioned in the paper.