= High-energy obstruction for a hard vector mass
{title2=$D_{\mu\nu}(k)=-i(g_{\mu\nu}-k_\mu k_\nu/m^2)/(k^2-m^2+i0)$}
A free <Proca field> is consistent and has three physical <particle polarizations>. The difficulty for generic interactions is the ultraviolet behavior of its <Proca propagator>: the longitudinal numerator makes part of it approach order $1/m^2$, rather than decay as $1/k^2$. Longitudinal external <polarization vectors> also behave as $\varepsilon_L^\mu=k^\mu/m+O(m/E)$. Without suitable identities and cancellations, amplitudes grow with energy and perturbative counterterms of increasing dimension are needed. Conserved-current Abelian models and the <Stueckelberg mechanism> are important exceptions; a massive interacting vector is not intrinsically inconsistent as an <effective field theory>.
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