Lorentz and Gauge invariance of EM

[AHSAN MUJTABA]

I have been reading the book of Chris Quigg, Gauge theories, Chapter 3, sec 3.3 in which he explains how local rotations transform wave function and variations in Schrödinger equation forces us to introduce the electromagnetic interaction between the particles. I need a bit deep concept of the ideas of gauge variance and invariance in electrodynamics. Kindly share some relevant material if possible as well.

 

[PeroK]

We may postulate an interaction between the electron and the EM field (as is done in classical EM). But, in QED, we may instead demand local gauge invariance. Neither the Dirac Lagrangian nor the EM Lagrangian is locally gauge invariance, but in combination with a relevant interaction term the total Lagrangian is.

This raises the possibility that local gauge invariance may be a fundamental law of nature.

And, when we apply the same principle of local gauge invariance to the quark model, we get the Lagrangian for QCD.

That means that, rather than having separate and arbitrary interaction postulates for QED and QCD, both theories may arise from the demand for local gauge invariance.

You might also take a look at Yang-Mills theory.

 

[AHSAN MUJTABA]

Thanks that helps.
I also need some details on Lorentz invariance of fields. TIA

 

[PeroK]

Thanks that helps.
I also need some details on Lorentz invariance of fields. TIA

There are Tong's notes on QFT:

https://www.damtp.cam.ac.uk/user/tong/qft/one.pdf

 

[AHSAN MUJTABA]

Thanks a lot