Feynman Diagram of a Coulombic Attraction?

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Discussion Overview

The discussion revolves around the representation of Coulombic interactions in Feynman diagrams, particularly focusing on the differences between electron-electron repulsion and proton-electron attraction. Participants explore the implications of virtual particles and their roles in these diagrams, questioning their physical significance and the mathematical framework behind them.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants note that Feynman diagrams can represent various interactions, including proton-electron attraction, but question how these diagrams would differ from those depicting electron-electron repulsion.
  • There is a discussion about the nature of virtual particles, with some arguing that they do not exist in a physical sense, while others suggest that their effects can be observed indirectly.
  • Participants debate the frame-dependence of virtual versus real particles, with references to concepts like the Unruh effect and Hawking radiation.
  • Some contributions emphasize that Feynman diagrams serve as mathematical tools rather than direct representations of physical processes, highlighting the complexity of quantum field theory.
  • There is mention of gauge dependence in the context of the Coulomb force, with discussions on how different gauges affect the representation of potentials in quantum field theory.
  • One participant expresses a desire to understand the mathematics behind Feynman diagrams better, indicating a personal journey in grasping the concepts discussed.

Areas of Agreement / Disagreement

The discussion contains multiple competing views regarding the existence and significance of virtual particles, the interpretation of Feynman diagrams, and the implications of gauge choice in quantum field theory. No consensus is reached on these topics.

Contextual Notes

Participants highlight that the concept of virtual particles is often debated, with some asserting that they are purely mathematical constructs while others argue for their indirect physical effects. The discussion also touches on the limitations of different gauges in representing physical phenomena.

  • #31
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 :)
 
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  • #32
tiny-tim said:
... 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.
 
  • #33
tom.stoer said:
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
 

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