Analogically, the unitarity of the theory of field $\psi $ in the most cases means, that field $\psi$ must transforms by the irreducible unitary representations of the Poincare group with mass $m$, momentum $p^{\mu}$ and spin $s$ (or with chirality $\lambda $ and momentum $p^{\mu}$). The unitarity requirement, of course, leads from QM postulate that the density of propability for particle is $\psi^{+}\psi$.

But if we don't connect fields with particles, we can analyze the non-unitary representations for fields.

This post imported from StackExchange Physics at 2014-03-23 12:07 (UCT), posted by SE-user PhysiXxx