Quantum physics doesn't use normalization much and these formulas work better without normalization. Normalization can be provided by the Bayes formula, so post

Quantum physics doesn't use normalization much and these formulas work better without normalization. Normalization can be provided by the Bayes formula, so postulating it is redundant. Also I heard QFT has some problem with global normalization, because everything must be local there, so normalization is replaced by Stokes' formula: the flux of state norm through closed spacetime surface is zero, i.e. the norm only conserves locally. And the evolution formula U(t)|0,0> = |1,t> + |2,t> can be seen as local conservation of the norm.