Weinberg book states the following (pg. 231):

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> "There is no problem in working with non-unitary representations, because the objects we are now concerned with are fields, not wave functions, and do not need to have a Lorentz-invariant positive norm"
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Schwartz book states the following (pg. 110 and 165)

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> "In addition we want unitary representation...."
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> "To construct a unitary filed theory we need unitary representation..."
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So my question is: is it strictly needed to have unitary representation of the Poincare' group? If it's so, what is the underlying reason?