Nonlinear, noncovariant spin-two theories

Physics

Scientific paper

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Fundamental Problems And General Formalism, Nonlinear Or Nonlocal Theories And Models

Scientific paper

Using Wald's 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 γab, and find a class of consistent theories which, when interpreted in terms of a metric, are invariant under the infinitesimal gauge transformation γab-->γab+∇(a∇cK||c||b), 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.

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