= Segal quantization criterion for fermions
{c}
{title2=$u\text{ implementable}\iff[P,u]\in\mathcal S_2$}
= Segal's quantization criterion for fermions
{c}
{synonym}
For the irreducible representation of the <canonical anticommutation relations> determined by $P$, a unitary one-particle map $u$ is unitarily implementable precisely when $P-uPu^*$ is <Hilbert-Schmidt>, equivalently when $[P,u]$ is Hilbert-Schmidt. The implementer is unique up to a scalar phase. The equivalent representation criterion for two polarizations is that their projections differ by a Hilbert-Schmidt operator. This yields a continuous <projective unitary representation> of the <restricted unitary group>.
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