Comment by ColinHayhurst
17 hours ago
Complex numbers and (Pauli/Dirac) matrices not required if you use Geometric Algebra. I highly recommend the book by Doran and Lasenby [0], or you can get the details from their papers, notably [1].
[0] Geometric Algebra for Physicists, CUP, 2003
https://deferentialgeometry.org/papers/Doran,%20Lasenby%20-%...
page 28, equation 2.36. Thanks a lot I'll take a dive into this
Note: my inquiry was motivated by this:
https://blog.revolutionanalytics.com/2014/01/the-fourier-tra...
p281 for Dirac equation. But I suggest you start at least from the beginning of Chapter 8. Earlier, obviously if you don't know Geometric Algebra. It's worth it; many examples but one is that the four Maxwell equations are expressed as one compact equation with geometric intuition.