What happens to a field after annihilation?

[Leo.Ki]

When an electron and a positron, for instance, annihilate, do their fields disappear away at c from the point of the annihilation, letting their former influence still apply beyond the vanishing line?

If the energy of these particles is entirely in their fields, as I sometimes read, how can the whole of their infinite fields instantly convert into gamma-ray photons or other particles without violating Relativity?

 

[CarlB]

Some would tell you that creation and annihilation operators are just a handy way of making QFT calculations.

Feynman expresses an opinion on the subject in his Noble prize speech:

I didn't have the knowledge to understand the way these were defined in the conventional papers because they were expressed at that time in terms of creation and annihilation operators, and so on, which, I had not successfully learned. I remember that when someone had started to teach me about creation and annihilation operators, that this operator creates an electron, I said, "how do you create an electron? It disagrees with the conservation of charge", and in that way, I blocked my mind from learning a very practical scheme of calculation.

http://nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html

Personally, I believe that they can, under certain circumstances, be assumed to be physical, and that they tell us some very odd things about the way that spacetime is assembled. One of the problems with this sort of belief is that gauge freedoms make it impossible to tell exactly what particles are created and annihilated.

Carl

 

[Careful]

One of the problems with this sort of belief is that gauge freedoms make it impossible to tell exactly what particles are created and annihilated.
Carl

Perhaps, the problem resides in the desire for manifest gauge freedom, in either the ``real'' thing cannot be gauge invariant at all (and there is nothing wrong with that).

Cheers,

Careful

 

[Leo.Ki]

Thank you Carl and Careful,
Your replies raise even more questions in my mind. I understand that annihilation and creation are actually misnomers for "mere" transformations, even if we don't work out what is transformed exactly. I even read once that an electron-positron pair isn't annihilated, and the two gamma-ray photons produced (in the low energy cases) only reflect the high kinetic energy of the collision after the two particles have accelerated into each other (the terminal kinetic energy being exactly the same as the rest energy of the particles).

 

[Rach3]

I should step in and point out the miscommunication that sprang up! Leo.Ki is asking about particle-antiparticle annihilation, but CarlB and Careful are talking about annihilation operators in QM and QFT. Two different things!

When an electron and a positron, for instance, annihilate, do their fields disappear away at c from the point of the annihilation, letting their former influence still apply beyond the vanishing line?

If the energy of these particles is entirely in their fields, as I sometimes read, how can the whole of their infinite fields instantly convert into gamma-ray photons or other particles without violating Relativity?

Strictly speeking, the annihilation is a quantum process and so you can only really deal with amplitudes, not precise, localized descriptions of the interaction step-by-step.. There is no "instantaneous" event to confound Special Relativity.

On the non-quantum perspective, note that the fields for two colliding point particles of opposite charge are very localized; in the COM frame for e+e-, the E field is that of a dipole and roughly cancels out at intermediate distances (no net charge!) (see picture here), likewise the B fields cancel out at intermediate distances (no net current!). So there is no difference between E/B fields for a positron&electron system and for two photons, unless you're very close to the situation, in which case quantum mechanics would confound you anyway.

A real explanation for what actually happens is somewhere in quantum electrodynamic theory.

 

[Careful]

I should step in and point out the miscommunication that sprang up! Leo.Ki is asking about particle-antiparticle annihilation, but CarlB and Careful are talking about annihilation operators in QM and QFT. Two different things!

No, I was not doing any such thing, I was merely responding to CarlB's thought whether what we call virtual particles in QFT could be considered as real physical entities (which is - I guess - what he meant by the phrase I copied). By the way, if you speak about particle creation/annihilation, you of course talk about the corresponding operators.

Careful

 

[Leo.Ki]

(...) So there is no difference between E/B fields for a positron&electron system and for two photons, unless you're very close to the situation, in which case quantum mechanics would confound you anyway.

A real explanation for what actually happens is somewhere in quantum electrodynamic theory.

Thank you Rach3, I like this idea of a smooth transition between two sets of particles/fields. The photons look a bit like the energy of the fields gone free to zip away in a concentrated form. Is it possible to swap the time and space axes and have an electron hit a gamma ray of equal energy and convert into a positron?
I guess I'll have to tackle QED in depth. Thanks!