Electron Self-Energy: QED Calculation & Verification

[blackie1008]

Hi,

I have been calculating the 3 infinities in QED as part of my project (vacuum polarisation, vertex corrections and electron self energy). Mostly I have been following the description in Mandl and Shaw for determining the first two (chapter 10, sections starting on p211). However it does not explicitly calculate, or state (as far as I can see) the result for the electron self-energy. I was wondering if there was anywhere that I could be pointed too so that I can check my result? I have been trawling the web, but to no avail...

Help would be much appreciated thanks!

 

[Drakkith]

Just wondering, what exactly is Electron Self Energy?

 

[RedX]

Just wondering, what exactly is Electron Self Energy?

The electron self-energy occurs in classical electrodynamics where if you calculate the potential of an electron at the point of the electron, you get infinity.

In classical electrodynamics this is ignored, but can be calculated in QED.

In QED the Green's function G(x,y) which represents propagation from spacetime point x to y (or the interaction of the field at x with the field at y) blows up when taken at the same point G(x,x). Note that such self-interactions are not taken into account in classical statistical mechanics.

G(x,x) is solved with renormalization.

The relationship between G(x,y) and the potential is:

V(r₁,r₂)=(2π)Integral d³k e^i(ki(x-y)i)G⁰⁰(k₀=0,k_i)