Interaction in QED: Electron/Proton Attraction & Repulsion

[paweld]

Why according to QED two electrons repel each oteher while
electron and proton attract. What are Feynman diagrams for
these proceses. Thanks for help.

 

[meopemuk]

Why according to QED two electrons repel each oteher while
electron and proton attract. What are Feynman diagrams for
these proceses. Thanks for help.

QED is capable of calculating only the S-matrix for the electron-electron or electron-proton scattering. So, from QED you can know amplitudes that connect asymptotic states (long before and long after the collision). Form these data you can indirectly figure out the type of interaction between colliding particles (i.e., attraction vs. repulsion). However, QED cannot tell you how exactly the particles move when they are in close proximity.

Eugene.

 

[paweld]

Thanks for your answer. I wonder if calculating S-matrix for electron-proton or
electron-electron scatering involves considering quantum nature of electromagnetic
field or we only assume that there is hamiltonian of interaction between these
particles (no exchange of photon is considered).

 

[meopemuk]

Thanks for your answer. I wonder if calculating S-matrix for electron-proton or
electron-electron scatering involves considering quantum nature of electromagnetic
field or we only assume that there is hamiltonian of interaction between these
particles (no exchange of photon is considered).

In traditional textbook QED the interaction Hamiltonian is a product of charged fields and the photon field. So, integrals for scattering amplitudes contain factors (photon propagators) that are obtained as certain matrix element of products of photon fields. In Feynman diagrams these propagators show up as wavy "photon lines". From this some people conclude that charges interact via "exchanges of virtual photons". But in my opinion this conclusion is completely arbitrary.

There is also a "dressed particle" formulation of QED in which the Hamiltonian of the electron+electron system does not contain photon contributions. In this approach, the electron-electron interaction can be interpreted as a direct instantaneous potential (Coulomb + corrections). The S-matrix computed in this approach is exactly the same as in the traditional renormalized QED.

Eugene.