I’m part of a geometric algebra working group at the Physical Institute of Heidelberg University. Currently, we’re creating an introductory lecture on geometric algebra for physicists which puts an emphasis on hands-on calculations, physical intuition and interfacing traditional math and GA.
The last two chapters are unfinished so far, but the rest is pretty much done already. If anyone here has any feedback, please do let me know! Also, you’re welcome to reuse the script for your own physics lecture courses on GA - I’d be happy to get in touch to discuss the specifics
Hi! I just looked at the lectures, and the chapter 7 has exactly the same problem as every other piece of physics literature on spinors has: the matrix representations are just handwaved in. As if Dirac and Weyl just happened to stumble upon some matrices that somehow match the generator properties of the algebra. There is no system to the representations.
But systematic representations actually exist, and one can find them using a variation of the Fast Fourier Transform!
This should have been a common knowledge at least since this work by P.Leopardi:
But, alas, it’s not. So I tried to contribute into spreading this knowledge too:
Please check it out! Hopefully this will make people a bit less confused about the matrix representations.
