NONLINEAR, NONCOVARIANT SPIN-2 THEORIES

Using Walds consistency criteria, we exhibit classes of nonlinear theories of a spin-two field that do not have general covariance. We consider the nonlinear generalization of linear equations of motion for a symmetric two-tensor field ab, and find a class of consistent theories which, when interpreted in terms of a metric, are invariant under the infinitesimal gauge transformation ab ab(acKcb), where Kab is an arbitrary two-form field. In addition, we find classes of theories that are conformally invariant. As a related problem, we compare the types of theories obtained from the nonlinear extension of a divergence- and curl-free vector field when it is described in terms of different choices of potential. It appears that the resulting types of nonlinear theories are not equivalent. A similar analysis is carried out for three-dimensional electromagnetism. © 1990 The American Physical Society.