I am looking at the following derivation of the Schrodinger equation: https://en.wikipedia.org/wiki/Schrödinger_equation#Derivation which clearly shows how the Schrodinger equation can be derived starting with $\psi(t)=U(t)\psi(0)$ and taking the Taylor expansion of $U(t)$.
Furthermore, at this link https://en.wikipedia.org/wiki/Wightman_axioms#W0_(assumptions_of_relativistic_quantum_mechanics) it states
One basic idea of the Wightman axioms is that there is a Hilbert space upon which the Poincaré group acts unitarily
My question, is can we get either QFT or RQM by taking
$$ \psi(t)=U(t)\psi(0) $$
where $U(t)$ is not a general unitary operator, but the unitary representation of the Poincaré group?
