recently when I was studying the scatterings which involves a vector boson (like W boson) as an intermediate particle, I saw that the propagator is not Lorentz invariant, I read that there is another source of Lorentz non-invariance in the Hamiltonian of the charged current. I mean the Hamiltonian is not simply the minus of the Lagrangian in this case h=-l. the extra term is not Lorentz invariant and, these two source of the Lorentz non-invariance will cancel each other eventually in the S-Matrix. (you can see :The standard Model, A primer written by Burgess chapters 4,5 and problem 5.4). I don't understand this completely, I'll be grateful if anyone can help me and explain it or introducing a reference for it.
I apologize for my bad English writing.