Interacting spin-two field on the light front

Abstract

The minimal (30-component) massive spin-two field is examined from the viewpoint of the Cauchy initial-value problem. The use of light-cone coordinates requires the existence of 25 independent constraints on the system, a number which is shown to obtain if one performs up to three successive differentiations of the primary constraint equations. These manipulations allow one to construct an algorithm for the evaluation of 25 dependent components in terms of a conveniently chosen set of five independent field variables. The introduction of an electromagnetic coupling is shown to result in a loss of some of the required constraint equations with two aspects of this breakdown being noteworthy. These are (a) the fact that (as in the spin-$\frac{3}{2}$ theory) the problem of obtaining the correct degrees of freedom can be solved if the condition ${F}_{\ensuremath{-}i}=0$ is imposed and (b) the loss of constraint occurs at the highest possible level, i.e., in the quaternary constraints rather than at the secondary or tertiary stages of the calculation.