Gauge Invariance and the Photon Self-Energy Correction

In summary, the conversation discussed the question of how gauge invariance forbids the photon mass in SUSY, without going through the full calculation. The concept of gauge invariance and Ward identities were mentioned as key factors in understanding this phenomenon. The individual asking the question also expressed a preference for a concise and mathematical explanation.
  • #1
shirosato
22
0
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
 
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  • #2
I do not know anything else but gauge invariance (classically) and Ward identities (after quantization).
 
  • #3
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.
 
  • #4
That's true
 

What is gauge invariance?

Gauge invariance is a fundamental principle in physics that states that the choice of gauge (a specific mathematical representation) should not affect the physical predictions of a theory. In other words, the physical laws should remain unchanged regardless of the gauge chosen.

What is the significance of gauge invariance in electromagnetism?

Gauge invariance is a crucial aspect of electromagnetism as it ensures the consistency and validity of Maxwell's equations, which describe the behavior of electric and magnetic fields. Without gauge invariance, these equations would not accurately predict the behavior of electromagnetic interactions.

What is the photon self-energy correction?

The photon self-energy correction is a quantum mechanical phenomenon in which the virtual particles in a vacuum interact with the electromagnetic field, causing a shift in the energy of the photon. This correction is necessary to account for the observed behavior of photons in experiments.

Why is the photon self-energy correction important?

The photon self-energy correction is important because it helps to explain the discrepancy between the theoretical predictions and experimental observations of the electromagnetic interactions. It also plays a crucial role in the development of quantum electrodynamics, which is the most accurate and successful theory of electromagnetism to date.

How is gauge invariance related to the photon self-energy correction?

Gauge invariance is closely related to the photon self-energy correction as it ensures that the correction does not affect the physical predictions of a theory. In other words, the correction must be gauge-invariant to maintain the consistency of the theory. This has been demonstrated in various calculations and experiments, confirming the importance of gauge invariance in understanding the photon self-energy correction.

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