Virtual Particle Anihilation

[alpha_wolf]

When a vritual particle pair anihilates, does the energy radiate away in the form of gamma rays, or is it simply used to "repay the debt" of whatever energy that was borrowed to create those particles in the first place? I would assume the latter, but I would like a confirmation on that. Thanks.

 

[zefram_c]

You are probably thinking of Feynman diagrams involving loops of virtual particles. IMO virtual particles have no physical existence, so they can't possibly annihilate to real particles.
Suppose you are thinking of a diagram in 2nd order QED, in which the intermediate photon momentarily splits into an electron/positron pair. The pair's effect is to modify the photon propagator (as well as introduce renormalization into the diagram)
You might also think of a diagram where one of the electrons emits a photon, then exchanges another photon with whatever is on the other side of the picture, then reabsorbs the first photon. This modifies some other property of the electron to second order.
Either way, it's better to think of their energy being returned to the vacuum (which is somewhat misleading), rather than having them annihilate to real particles - the latter is patently impossible.

 

[marlon]

The pair's effect is to modify the photon propagator (as well as introduce renormalization into the diagram)
Either way, it's better to think of their energy being returned to the vacuum (which is somewhat misleading), rather than having them annihilate to real particles - the latter is patently impossible.

Yes in QFT this effect is also called the vacuum polarization and one has to introduce the polariztion-insertion into the foton propagator. it is the self-energy of the foton propagator and the main fysical consequence is that the vacuum is replaced by some kind of dielectricum, which is able to influence elektromagnetic-interactions going on.

Virtual particles are also the counterterm to the infinities of the bare particles. So the total adds up to a finit value. dressed particles = bare particle + cloud of virtual particles. Self energy express to what extent a bare particle is able to make some of these virtual particles real and by doing so energy-conservation is violated.