Tuesday, 3 September 2019

quantum electrodynamics - How to get Hamiltonian of QED from lagrangian?


I have the QED lagrangian: L=ˉΨ(iγμμ+qγμAμm)Ψ+116πFαβFαβ.

I tried to get hamiltonian by getting zero component of energy-momentum tensor: Tμν=iˉΨγμνΨ+14πFμγνAγ14πJμAν
T00=iΨ0Ψ+14πF0γ0Aγ14πJ0A0=iΨ0Ψ+14πF0γ0Aγ14πΨA0Ψ=Hdensity.
But it seems that it's incorrect, because I never get by this expression term ˉΨγμΨAμ, which refer to interaction part.


So how to find the true hamiltonian?


Thank you.



Added. Hmm, I find the mistake in expression of energy-momentum tensor. Fixed.




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