# Feynman Diagram of a Coulombic Attraction?

1. Jun 9, 2010

### mk17

Whenever I see examples of the diagram for the Coulomb interaction it always seems to be two electrons interacting via an electron and being repulsed. The diagram looks intuitive in terms of momentum conservation.

I was wondering how (for example) a proton - electron interaction, and subsequent attraction, would be drawn? Does the electron still emit a photon in the direction of the proton?

Thanks.

2. Jun 10, 2010

### tiny-tim

Welcome to PF!

Hi mk17! Welcome to PF!
(you meant "via a photon" )

"the diagram" ?

There's no such thing as "the diagram" for an interaction … there are infinitely many diagrams for the same interaction, of which that one is simply the simplest.
The Feynman diagrams would be the same.

But the virtual photons and virtual electrons in the middle of the diagrams (twice as many electrons as photons in most of the diagrams) don't repel or attract, beacuse they don't exist

virtual particles don't exist (the clue's in the name ), they're just maths.

3. Jun 10, 2010

### Dmitry67

There difference between virtual and real particles is frame-dependent. Those who deny the existence of virtual particles should also deny the existence of 'real' ones.

4. Jun 10, 2010

### tiny-tim

Hi Dmitry67!
uhh?

Are you saying that there is a frame in which the virtual photons and virtual electrons in a Feynman diagram for electron-electron repulsion are real?

5. Jun 10, 2010

### nrqed

What do you mean? A virtual particle is one for which

$$P_\mu P^\mu \neq m^2$$

and this is a frame independent statement.

6. Jun 10, 2010

### Dmitry67

In some accelerated frames they are real. Different accelerated frames don't agree on the number of real and virtual particles of the same macroscopic events. Check Unruh effect for example. Hawking radiation is another one (free falling body does not see that radiation).

My personal opinion: Feynman Diagrams describe what is actually happening. Sum on infinite number of histories. However, as there is no collapse and measurement, there are no 'real' particles, no incoming particles and no particles which go away to be 'registered'. Our world is just one infinite Feynman diagram without borders.

7. Jun 10, 2010

### tiny-tim

Are you saying that there is an accelerated frame in which the virtual photons and virtual electrons in a Feynman diagram for electron-electron repulsion are real?

8. Jun 10, 2010

### Dmitry67

No, because if they participate in the repulsion, then they go from one particle to another without any absorption -> they could not leave any tracks (there are cases however when virtual particles create some macroscopic effects)

But, on the other hand, claim that 'they are just pure mathematics' is too strong.

9. Jun 10, 2010

### tiny-tim

Sorry, but that doesn't make any sense … what does "without any absorption" mean, and what does an accelerated frame have to do with it?

10. Jun 10, 2010

### Dmitry67

Ok, I was trying to say that these virtual photons can not be registered directly, but their effects are registered indirectly. But it is not enough to say that they are 'not real' and 'pure mathematics'.

For example, wavefunction itself can't be registered directly. However, in many interpretations wavefunction is real. So the claim 'virtual particles are pure mathematics' for me is equivalent to Copenhagen Interpretation (where it was valid, and as CI was dominating for a long time, people got used to that point of view).

11. Jun 10, 2010

### Dickfore

Feynman diagrams do not sketch a real world situation where particles collide. They are a pictorial way of representing complicated mathematical expressions in terms of a few primitive objects (propagator, vertex, external source).

12. Jun 10, 2010

### tiny-tim

hmm … I notice that you're now ignoring the virtual electrons in the same interaction …

there are twice as many virtual electrons as virtual photons in most of the diagrams …

I suspect that you've heard that the electromagnetic field is "mediated by" photons, and so the virtual electrons in the diagrams somehow don't "mediate" it.

Well, as Dickfore says, Feynman diagrams are a pictorial representation of mathematical expressions. Virtual photons and virtual electrons participate in the same way, and since an infinite number of diagrams is needed, so an infinite number of virtual particles is needed … so how many virtual photons and electrons do you think there are when two real electrons repel, and when do they appear?

13. Jun 10, 2010

### Dmitry67

Whats about the repulsion between, say, 2 electrons with not only 1 virtual photon, but including the loop of virtual e+/e-? and (on very short distances) even t+/t- (top quarks)? Or even ?+/?-, where ? is not-yet-discovered supersymmetric particle? Why that 'pure mathematics' mimics the 'real' world so literally?

14. Jun 10, 2010

### xepma

If we had a way of determining quantum amplitudes directly (scattering processes, the ground state of a system or just the propagation of a particle), we would never need the concept of a virtual particle. It's just a mathematical side of perturbation theory. For example, in some integrable quantum field theories (e.g. certain conformal field theories) you do not need perturbation theory so to whole concept of Feynman diagrams and 'intermediate' states is completely circumvented! The concept of a virtual particle (= 'intermediate' state) never pops up!

Perturbation theory, in the end, is nothing but trying to solve an interacting theory using a non-interacting formulation -- completely similar to using a Taylor series to approximate an analytic function. The different terms in the Taylor expansion is similar to the different Feynman diagrams (which contain the virtual particles) in the perturbation series ...

15. Jun 10, 2010

### tom.stoer

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.

16. Jun 10, 2010

### xepma

That gauge choice actually named after Ludwig Lorenz (no t!), and not Hendrik Lorentz ;-)

17. Jun 10, 2010

### tom.stoer

correct; sorry for that

18. Jun 10, 2010

### mk17

Re: Welcome to PF!

I did indeed, oops.

Anyway, thanks for the replies everybody, obviously I was thinking Feynman diagrams have a physical significance that they don't.

Eventually, hopefully, I'll be competent enough to understand some of the mathematics behind them and actually be able to use them!

19. Jun 10, 2010

### alxm

The idea of using diagrams for perturbation theory spread to different areas either, so quantum chemistry has e.g. Hugenholtz diagrams and Goldstone diagrams.

20. Jun 11, 2010

### Dmitry67

In SM - yes.
But it is just one interpretation.