Getting rid of negative norm states

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In Warren Siegel's Fields page 131 , He says that in order to get rid of the negative norm zero component of the vector wavefunction , we impose the constraint $S^{a}_{b}P_{a}+\omega P_{b}=0$ in analogy to the on-shell constraint $P^2+m^2=0$. I don't see how this can help us get rid of negative probability wavefunctions.

A constraint is an additional equation. Consider this constraint in the rest reference frame (${\bf{P}}=0$). It is imposing a certain value to an otherwise "arbitrary" or "independent" wave function component.  If the negative norm component becomes zero due to this condition, it stays "harmless" in the other reference frames due to relativistic invariance of expressions involving this norm.
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