Wednesday, January 10, 2018

quantum field theory - How to arrive at the Dirac Equation from Poincaré Algebra?


For the case of Galilean group, the time translation is given by the generator H. Hence, ψ(t)→∣ψ(t+s)=eiHsψ(t) Which immediately is the Schrödinger equation, ddtψ(t)=iHψ(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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