The formulation of quantum mechanics that I've read deals with commutators of generators of the symmmetries of the galilean group, and the physical interpretation of these generators. My education in QM isn't particularly great, and I can't be bothered to sit and work it out myself, but I was wondering what result is obtained if instead of the galilean group one uses the Lorentz group? Does this lead to anything familiar to QED or does it simply produce results not too different to those of non-relativitistic quantum mechanics? The derivation of QED I'm familiar with is through quantising Maxwell's equations of classical electrodynamics.

 

Thanks guys

Funnily enough, I am just teaching a course on relativistic quantum mechanics. It is a bit waffly because I wasn't allowed to use QFT, but the pdf is here:

http://www.physics.gla.ac.uk/~dmiller/lectures/RQM.pdf

 

(Please don't email me.)