Weak Electron Interaction: Virtual Photon Effects?

[scope]

hi, let's suppose 2 electrons are far away each other and therefore they interact very weakly. i wonder if in such case there are as many virtual photons in the case they are very close to each other? because i know that only 1 electron in complete vacuum generates an electromagnetic field and therefore virtual photons . please reply!

 

[strangerep]

hi, let's suppose 2 electrons are far away each other and therefore they interact very weakly. i wonder if in such case there are as many virtual photons in the case they are very close to each other? because i know that only 1 electron in complete vacuum generates an electromagnetic field and therefore virtual photons .

The most important thing to grasp is that virtual photons are unphysical.
They're essentially just terms in a perturbation expansion.

You might as well ask whether, when two combatants glare at each other,
are there more virtual daggers flying between their eyes when they're close
together than when they're far apart?

It's all a bit silly, really.

 

[scope]

hi, i do know that they are not physical, but it seems to me logical that further interactions means further virtual photons. if there are more virtual photons that are exchanged and all the rest remains the same, then there are more virtual photons.
the question is whether the intensity(or number) of virtual photons is measured by the field (not really the interactions) or the force(the intensity of interactions)?

 

[jtbell]

It seems to me that every electromagnetic interaction involves an infinite number of virtual photons. To calculate the amplitude for any interaction exactly, we have to sum up an infinite number of terms in the perturbation expansion, each of which has its own Feynman diagram. Higher-order Feynman diagrams include more and more virtual photons.

 

[tom.stoer]

One can formulate QED in Coulomb gauge which contains the Coulomb potential w/o any sumation over radiative corrections. One has to use the appropriate gauge for this problem.

It is a common misconception (which I see quite often here in the PF) that QED does contain only perturbative photons. This is not correct in general.

 

[kexue]

One can formulate QED in Coulomb gauge which contains the Coulomb potential w/o any sumation over radiative corrections. One has to use the appropriate gauge for this problem.

In which book is that done?

 

[tom.stoer]

Please refer to the following article:

Quantum Mechanics of Gauge Fixing
Lenz F., Naus H. W. L., Ohta K. and Thies M.
Annals of Physics
Volume 233, Issue 1, July 1994, Pages 17-50
Abstract:
In the framework of the canonical Weyl gauge formulation of QED, the quantum mechanics of gauge fixing is discussed. Redundant quantum mechanical variables are eliminated by means of unitary transformations and Gauss′s law. This results in representations of the Weyl-gauge Hamiltonian which contain only unconstrained variables. As a remnant of the original local gauge invariance global residual symmetries may persist. In order to identify these and to handle infrared problems and related "Gribov ambiguities," it is essential to compactify the configuration space. Coulomb, axial, and light-cone representation of QED are derived. The naive light-cone approach is put into perspective. Finally, the Abelian Higgs model is studied; the unitary gauge representation of this model is derived and implications concerning the symmetry of the Higgs phase are discussed.