# Peeter Joot's (OLD) Blog.

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## interesting lecture on classical and quantum relations for electrons.

Posted by peeterjoot on March 18, 2009

I listened to a recorded lecture today by Baylis on electron spin related via active lorentz transformations to spinors, and found his paper on arxiv. It’s timely since I’ve been working on understanding both QM and E&M, and I’d like to see some of the big picture of how these fit together.

Baylis uses a complex (quaternion like) representation that I’ll probably have to translate for myself to STA or tensor form to get a feel for things. Will see how the reading of his paper goes if this is actually neccessary.

Although he didn’t mention it, I believe that he’s also covered the acceleration bivector of GAFP in his lecture where he wrote the Lorentz force equation as $\dot{p} = scalar(\Omega u)$. Something clicked for me when I saw that … it looks just like the $\Omega \cdot \mathbf{v}$ of rotational dynamics (as in Tong’s notes, or in Goldstein). Following Goldstein or Tong, this could all probably be formulated in matrix form in index notation utilizing an antisymmetric tensor. Is there a clean representation of rotors in tensor form (ie: the exponentials)?