Propagator of a massive spin-3 field

The Lagrangian matrix Λ(p) of a massive spin-3 field proposed by Kawasaki and Kobayashi is fully inverted to give the correct propagator. The three parameters contained in Λ(p) are kept arbitrary throughout the calculation. It is stressed that in the local covariant Lagrangian approach the propagator should be the strict inverse matrix of Λ(p). The reason for this is well illustrated by an example of a massive spin-2 theory. In so doing, we point out the following facts: (1) Since the Lagrangian given by Singh for a massive spin-2 particle is equivalent to that given by Bhargawa and Watanabe, for which the propagator is known, the propagator of the former is obtained from the latter by a simple transformation. (2) Although the auxiliary components appearing in high-spin field theories vanish because of the Euler-Lagrange equation, they have a finite contribution to the S-matrix elements through covariant T products, which are in general nonvanishing. (3) The generalized Matthews rule is naturally supported by the path-integral prescription. (4) After eliminating the auxiliary components by a path integral, we have an effective nonpolynomial Lagrangian matrix, which is the inverse of the ''partial propagator'' previously obtained by many authors