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The quantum mechanical time evolution operator governs how observables and/or states evolve during finite time steps, and is always unitary. Use this tag for questions about the time evolution operator, or the different equations of motion in the Schrödinger/Heisenberg/Dirac pictures. For time-independent Hamiltonians, the time evolution operator is simply exp(-iHt).
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Time evolution vs. Time translation in QFT
I think I have figured it out. Everything I wrote is correct up till I identified:
$$\hat{U}(t) = U(\Lambda = 1, a^\mu = (\Delta t,0,0,0))$$
While is is true that we have:
$$U(\Lambda = 1, a^\mu = (\D …
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Time evolution vs. Time translation in QFT
There is a certain sign mismatch between the time translation operator and time evolution operator in quantum field theory which I hope someone can illuminate.
From my understanding, a Poincaré transf …