|WikiProject Mathematics||(Rated Start-class, Mid-importance)|
looks like a redundant page.
I have taken the whole of the second section and copied it verbatim to Gamma matrices (same as Dirac matrix and would suggest that this page could be deleted Selfstudier (talk) 00:40, 13 November 2010 (UTC)
Keep it as a stub. I have plans about fleshing it out that would be too much to put in Gamma matrices. (That one could move here though if and when this becomes good.) YohanN7 (talk) 09:52, 29 September 2012 (UTC)
The algebra and the matrices are not the same thing. And Dirac algebra is potentially at odds with Gamma matrices (or at least has the scope to generate confusion) in this regard. In particular, the latter gives the real Clifford algebra Cℓ1,3(R) as what is generated by the matrices (which is true for the if the scalars are taken as the real numbers, even when the matrix entries are complex, but false for if the scalars are taken as the complex numbers). What is important is that there is evidently an algebra called the Dirac algebra and this (which, I guess, is Cℓ4(C)) and this definition of the abstract algebra should not be lost. — Quondum 13:45, 29 September 2012 (UTC)
- That's good arguments for keeping the articles separate. Then whether Cℓ1,3(R) or Cℓ3,1(R) gives the gamma matrices is a matter of which convention is adopted for the Lorentz group, O(3;1) or O(1;3). If you pick up a text at random, then Murphy's law guarantees that it uses "the other" convention. B t w, I'm not going to do anything with this article in the near future. Maybe in a couple of weeks. YohanN7 (talk) 15:02, 29 September 2012 (UTC)
- Of course, Gamma matrices naturally uses "the other" convention compared to Representation theory of the Lorentz group. Sigh... There is a need to have a central separate article on stuff of this sort. The problem manifests itself everywhere where it possibly could (by Murphy's law again). Lie algebras are the prime examples, followed by the Lorentz metric. YohanN7 (talk) 15:18, 29 September 2012 (UTC)