= Nonzero-momentum condition in the massless vector norm test
{title2=$p=0,\ a=1/2,\ A=(1,0,\ldots)\ \Rightarrow\ A^*\cdot A=-1$}
The usual half-level NS claim that all physical vector polarizations have nonnegative norm for $a\le1/2$ assumes nonzero particle momentum. At zero momentum and limiting intercept, all positive-mode <constraints> and transversality allow a timelike polarization with negative norm, and $A\sim A+\kappa p$ removes nothing. Excluding this exceptional momentum restores the ordinary null-vector argument; retaining it makes the unrestricted elementary criterion strict $a<1/2$.
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