Supermultiplets and relativistic problems: I. The free particle with arbitrary spin in a magnetic field

Abstract

Equations for relativistic particles for arbitrary spin have been of interest since Dirac original work for spin , but they involved either bothersome constraints or start with as many Dirac equations as are required to get the derived spin from its original value. We first show that it is possible to have just one equation involving 's and 's matrices that give possibilities up to for the spin. We then decompose the 's and 's into direct products of ordinary spin matrices and a new type of them that we call sign spin. The problem reduces then to one in terms of the generators of a U(4) group entirely similar to the one in the spin - isospin theory of nuclear physics and hence the name of supermultiplets in the title. Using then the techniques of the latter we discuss the problem of a free particle in a magnetic field for n = 1,2 and 3 or equivalently eigenvalues for spins 0,, 1 and , and the energies are given as solutions of elementary algebraic equations.