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nrqed

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It is clear that we won't make progress unless we look at a specfic Feynman diagram because I am saying that the total energy in the intermediate state is equal to the initial energy and you are saying that it is not. So we just have to write down the expression for a Feynman diagram and see!!! Let's apply the Feynman rules, look at the intermediate state (in which there are virtual particles), add up their energies and see what happens! Otherwise, it's no different than being indoors and arguing "the sky is blue" "no, the sky is orange" "no the sky is blue" "no, the sky is orange!" and so on, without going out and looking at the darn skymarlon said:Well, here's our fundamental difference. In my second post here, i clearly stated that total energy conservation applies to the initial and final state and NOT the intermediate state. In QFT, thanks to this violation of total energy conservation many interactions exhibit the following property : Due to the existence of virtual particles (which DO NOT exist in the initial state for the obvious reason) there is more "total" energy than in the initial state. Many such interactions are known in QFT and this can only exist if energy conservation is violated during the period between initial and final state. It is in this period that interactions with the vaccuum can occur as well. If this were not possible, concepts like the vacuum polarization tensor would not exist or be usefull.

I am really not sure what "during vertex points" means. I still argue that if four-momentum conservation is imposed at all vertices, then four-momentum will be conserved in all intermediate states.This is not the point. We are talking about the spread of energy that exists during vertex points !

The simplest example I can think of is the one-loop vacuum polarization diagram. Photon goes to an electron-positron virtual pair and this pair turns back into a photon. If we call q_0 the energy of the initial photon, the sum of the energy of the electron-positron will be q_0, for any loop momentum. Do you disagree with that?? (notice that the energy of a virtual particle is the zeroth component of its four-vector. One cannot use [itex] {\sqrt{m^2- {\vec p}^2}}[/itex] since it is not on-shell)

Or if you prefer, take the scattering of an electron off an external em field. There are 4 diagrams to one loop (vertex correction, mass renormalization on the two external electron lines, vacuum polarization on the photon line). Pick any intermediate state and we'll calculate the total energy to see.

tehn how can one ever write down an expression for a Feynman integral? The propagator for a photon, say, is 1/q^2. So if the momentum of a virtual photon is not defined, how can we get anything calculated?No, one cannot speak about the four momentum of particles in intermediate states since energy is uncertain. Also, many interactions are known (i gave an example) where this is not true. What you state here is totally contradictory.

regards

marlon

Regards,

Patrick

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