Dynamical inconsistency and conformai covariance of the massless tensor field

Abstract

By means of the recently found Lagrangian for the Nordstrom theory of scalar gravity we write down the conformal-invariant field equations of the massless tensor field, as the field equations of the minimal interacting system composed by the spin-2 massless field and the scalar-gravity field. These equations constitute a good example of the well-known complexivies arising when one is dealing with higher-spin (> 1) fields, whether in an external field or interacting with another field. In the present case it is shown that the massless tensor field considered as imbedded in an external scalar field has a different number of degrees of freedom than if it is considered as a part of the whole interacting system. This is achieved by analysing the evolution of a perturbation on a nontrivial background solution (a pure spin-2 plane wave). It is also shown that secondary constraints do not vanish identically as a consequence of the already studied loss of the Ricci-like identity.