Consequences of a Field-Source Identity in a Spin-2 Meson Theory

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Abstract
We discuss the restrictions imposed on a spin‐2 meson theory when the source is related to the stress tensor. We consider a spin‐2 meson theory with a field‐source identity, which postulates that the traceless part of the stress tensor is proportional to the irreducible part of the spin‐2 meson field. We examine the consequences of imposing the field‐source identity and Lorentz covariance on the spin‐2 meson theory. We show that the field‐source identity determines the parts of the singular terms in the stress‐tensor equal‐time commutation relations which are the most singular in the coupling strength g. It further requires that some of the singular terms be q‐numbers. We obtain the constraints imposed on the field‐dependence of the source Jμν(x) by the field‐source identity and the Lorentz covariance conditions. We show that as a consequence of some of these, the interaction term gJμν(x) must be nonlinear in the coupling strength g.

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