I have the QED lagrangian: L=ˉΨ(iγμ∂μ+qγμAμ−m)Ψ+116πFαβFαβ.
I tried to get hamiltonian by getting zero component of energy-momentum tensor: Tμν=iˉΨγμ∂νΨ+14πFμγ∂νAγ−14πJμAν⇒
T00=iΨ†∂0Ψ+14πF0γ∂0Aγ−14πJ0A0=iΨ†∂0Ψ+14πF0γ∂0Aγ−14πΨ†A0Ψ=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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