For the case of Galilean group, the time translation is given by the generator H. Hence, ∣ψ(t)⟩→∣ψ(t+s)⟩=e−iHs∣ψ(t)⟩ Which immediately is the Schrödinger equation, ddt∣ψ(t)⟩=−iH∣ψ(t)⟩ How to arrive at the Dirac Equation from the Poincaré Algebra/Group? I know it will be much more involved. I am not expecting answers that say how Dirac thought of it or trial and error nonsense.
The necessity for Dirac equation should be visible from the Poincaré Algebra/Group?. How does spin come into the picture?
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