A note on the minimal electromagnetic interaction of spin-two particles

Abstract

During the last couple of years, VRLO and ZWANZIGER (1) have investigated the problems arising in the interaction of higher-spin particles interacting with the electromagnetic field via minimal interaction. In particular, for spin-two particles, one of the results that emerge from their work is that the number of degrees of freedom of a spin-two particle interacting with an electromagnetic field increases to six, which is one more than in the free-field case. This result is already contained implicitly in an earlier paper by ~:EDERBUSH (2) who also suggested the use of nonmiuimal terms in the interaction to recover the correct number of degrees of freedom. The purpose of this note is to show that there exist spin-two Lagrangians which yield equations of motion that are stable as far as the number of degrees of freedom is concerned when electromagnetic interaction is introduced via minimal replacement. A similar result has already been pointed out by HAGEN (a) in the context of linearized Lagrangians. We, however, work with the second-order formalism. We start by writing the free spin-two Lagrangian considered by VELO and ZWANZIGF~R (1) ;