0 v 1 1 9 A ug 1 99 9 Pair production and solutions of the wave equation for particles with arbitrary spin ∗

We investigate the theory of particles with arbitrary spin and anomalous magnetic moment in the Lorentz representation (0, s) ⊕ (s, 0), in an external constant and uniform electromagnetic field. We obtain the density matrix of free particles in pure spin states. The differential probability of pair producing particles with arbitrary spin by an external constant uniform electromagnetic field has been found using the exact solutions. We have calculated the imaginary and real parts of the Lagrangian in an electromagnetic field that takes into account vacuum polarization.