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I am currently preparing a talk about Clifford algebras and pin/spin-groups. Since half the audience will consist of physicians (as I am myself) I also want to get more into the connection of the mathematical definitions and derivations (as one may find in Baker, "Matrix groups" or, more for the physical liking, "Analysis, Manifolds and Physics (vol. 2)" of Choquet-Bruhat Y. & Dewitt-Morette) to the physical tools of everydays use, like Weyl-spinors, Majorana representation, behaviour of spinors under rotations.

Especially the last point is unclear to me. The only somewhat good explanation I could find was in Wikipedia, article "Spinor" (http://en.wikipedia.org/wiki/Spinor" [Broken]). Under >> "Examples" >> "Two dimensions" it is written that the action of elements on vectors is

[tex]\gamma\left(u\right) = \gamma u\gamma^*[/tex]

whereas on spinors it is

[tex]\gamma\left(\phi\right) = \gamma \phi[/tex].

So the spinor shell be just a complex number. But where do these actions come from? What distinguishes, in this special case, vector and spinor? I am somewhat confused.

Thanks everybody helping me out!

Blue2script

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# Action of Clifford-elements on vectors & spinors

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