Two-point functions of local infinite-component fields

An explicitly covariant technique is used to derive a representation for the two-point function $F_{\varphi\psi}(x-y)=\langle0|\varphi(x)\psi(y)|0\rangle$ which takes into account Lorentz covariance, the spectralcondition, and locality; the fields $\varphi$ and $\psi$ may transform in accordance with arbitrary irreducible representations of the proper Lorentz group. The method can also be applied to local nonrenormalizable theories (in which the two-point functions in momentum space may have a growth faster than polynomial). As a corollary it is proved (without any “technical assumptions”) that the mass spectrum in a theory of local infinite-component fields is infinitely degenerate with respect to the spin. By the same token, the well-known Grodsky–Streater “no-go” theorem is extended to nonrenormalizable theories.