Why is it interesting?

Layman?

Student

Now that I’ve convinced you that gauge invariance is misleading, let me unconvince you. It turns out that the gauge fixing in Eq. (97) is very special. We can only get away with it because the gauge symmetry of QED we are using is particularly simple (technically, because it is Abelian). When we do path integrals, and study non-Abelian gauge invariance, you will see that you can’t just drop a gauge fixing term in the Lagrangian, but have to add it in a very controlled way. Doing it properly leaves a residual symmetry in the quantum theory called BRST invariance. In the classical theory you are fine, but in the quantum theory you have to be careful, or you violate unitarity (probabilities don’t add up to 1). Ok, but then you can argue that it is not gauge invariance that’s fundamental but BRST invariance. However, it turns out that sometimes you need to break BRST invariance. However, this has to be controlled, leading to something called the Bitalin-Vilkovisky formalism. Then you get Slavnov-Taylor identities, which are a type of generalized Ward identities. So it keeps getting more and more complicated, and I don’t think anybody really understands what’s going on.

http://isites.harvard.edu/fs/docs/icb.topic473482.files/08-gaugeinvariance.pdf

Researcher

Common Question 1

Common Question 2

Examples

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Example2:

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