The Dirac oscillator of arbitrary spin

The problem of a relativistic particle with an arbitrary spin has had an old and distinguished history, particularly if the particle is free or interacting with an electromagnetic field. Recently a new type of interaction, denoted as the Dirac oscillator, has been introduced, first for particle of spin 1/2 and later for spins 0 and 1, and it has suggested a possible generalization to arbitrary spin. Following a procedure originally developed for a system of n particles with spin 1/2 with a Dirac oscillator interaction, we have derived a single particle equation with spins in the range 1/2n:1/2n-1:...:1/2 or 0 and through a symmetric representation of the permutation group restricted it to spin . We have solved the resulting equation explicitly by reducing it to an algebraic one in the energy E, whose coefficients depend on the number of quanta N, the total angular momentum j and the frequency ω of the oscillator. Properties of the energy spectra will be discussed for spins 1/2, 1, 3/2. (author)