Feynman Diagram of a Coulombic Attraction?

[Dmitry67]

tom, thank you, interesting. The number of additional quark-antiquark pairs participating in very short pocesses is not a surprise at all. I hope tiny-tim can tell 'real' quarks from 'virtual' ones inside the proton :)

 

[tom.stoer]

... but there are perfectly good theories in which the electron obviously does have a position, and there is a definite number of electrons …

Can you tell me which theory you are talking about?

Can you tell me how to proof that the number of electrons in QED is fixed? It will not work, simply because the operator counting the number of electrons does not commute with the Hamiltonian of QED.

 

[reilly]

The concept of Coulomb force is gauge dependent!

In the Lorentz gauge you will not see a Coulomb potential at all. In Coulomb gauge (that's where it's name is coming from) there is a "photon term" plus a static Coulomb potential term" in the Hamiltonian. So the static Coulomb potential is not due to virtual photons but looks exactly as in electrostatics.

The choice of the gauge is arbitrary, but it should fit to the problem you want to study. For (relativistic) scattering experiments the Lorentz gauge is nice, but e.g. for Lamb shift calculations it's awful.

>>>>>>>>>>>>>>>>>>>>>>>>>>

Not true at all. E&M allows various gauges for potentials, but not for forces. Now, experiment demonstrates that charged particles, moving slowly, exert Coulomb forces on each other. Thus, no matter what gauge is involved, there must be a Coulomb potential to generate this force -- as is demonstrated in potential theory, and, for that matter, in freshman physics. Any relativistic theory of EM regardless of gauge, classical or quantum, must have a NR limit of Coulomb interactions. And, it thus becomes evident, a single photon exchange generates this interaction -- see Yukawa's explanation of meson exchange as a generator of nuclear forces.

Note also, that a charged particle exerts only a Coulomb interaction in its rest frame. However, the exact solutions, Coulomb wave functions for an NR electron scattering in a Coulomb field, don't indicate anything like photon exchange. So, ...

Virtual particles real? Well, consider the photoelectric effect. Clearly, the ejected electron is not on its mass-shell when inside the metallic target. Yet, who would say that this electron does not exist prior to ejection?

Regards,
Reilly Atkinson