Gauge Invariance and the Photon Self-Energy Correction

[shirosato]

Short intro.: I'm a 2nd year M.Sc. student in particle physics, with basic quantum field theory and knowledge of the SM and perhaps a bit more. I've read the forums before and tried to find questions/answers that were similar to my own until I decided, "why not just join so I can ask exactly what I want to know?"

Anyway, my question is this: in most introductions to SUSY, they go over the self-energy diagrams for the photon/gauge boson as well as the electron. They then give some simplified integral representing the correction and then saying that gauge invariance guarantees that the correction identically vanishes.

This makes sense knowing some gauge theory (gb mass terms break gauge invariance) and they often cite the Ward identities. Without going through the whole calculation, is there any easy way to explain how gauge invariance forbids the photon mass that is somewhat mathematical without going the whole mile? Writing this, it sounds lazy, but I honestly like to have the minimal non-hand-wavey solution handy at all times.

Shirosato

 

[tom.stoer]

I do not know anything else but gauge invariance (classically) and Ward identities (after quantization).

 

[shirosato]

Well, upon a bit more reading, its basically outlined in 245-246 of Peskin and it seems that its basically, the gauge invariance of qed manifests itself through the ward identities.

 

[tom.stoer]

That's true