Coulombs law derivation

  • #1

Main Question or Discussion Point

How the virtual photon exchange theory be used to derive completely Coulombs Law related to electrostatic field? Complete derivation means derivation involving charges and distance
 

Answers and Replies

  • #3
tom.stoer
Science Advisor
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You don't need any virtual photons but you can derive Coulombs law w/o using perturbation theory. It's most transparent in
a) Coulomb gauge or in
b) A°=0 gauge plus fixing of the residual symmetry of time-independent transformations respecting A°=0.

In both cases it boils down to construct the inverse of the Laplacian 1/Δ; in Coulomb gauge this is due to the Poisson equation

[tex]\Delta A^0 = \rho[/tex]

with

[tex]\Delta^{-1} \to k^{-2} [/tex]

in k-space and

[tex]\Delta^{-1} \to |x|^{-1} [/tex]

in x-space

This results in an interaction term

[tex]V \sim \int d^3x\,d^3y\,\frac{\rho(x)\,\rho(y)}{|x-y|} [/tex]

Of course there are other interaction terms involving physical (transversal) photons as well.
 
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