= Intrinsic time-reversal phase
{title2=$|\eta_T|=1,\quad\eta_T\mapsto e^{-2i\chi}\eta_T$}
In the scalar transformation $\hat Ta(p)\hat T^{-1}=\eta_Ta(p_P)$, preservation of canonical commutators or the involution condition gives $|\eta_T|=1$. <Antiunitarity> conjugates the phase on a second application, so the condition does not restrict it to plus or minus one. Redefine $a'=e^{i\chi}a$; then $\hat Ta'\hat T^{-1}=e^{-2i\chi}\eta_Ta'(p_P)$. Choosing $\chi=\arg(\eta_T)/2$ makes the intrinsic phase one. Oppositely rephasing the <antiparticle> annihilator implements the same change as a phase convention for the whole scalar field.
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