Talk:Dirac equation in the algebra of physical space

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Is this article needed ?[edit]

I seriously question the need for writing a whole article on the Dirac equation using a certain formalism - also, this can easily get out of hand: articles on Einstein's equations using various formalisms, Schrodinger equation etc... ? Let's not fall into the trap of writing a textbook here (there are other places where that can be done - Wikibooks). If this topic needs to be discussed, then surely it can be included in the Dirac equation article itself. MP (talk) 09:02, 4 February 2006 (UTC)[reply]

This article will be part of the wikibook

http://en.wikibooks.org/wiki/Physics_in_the_Language_of_Geometric_Algebra._An_Approach_with_the_Algebra_of_Physical_Space [[User::cabrer7]] February 24 2006

I am the original author of this article. After some positive feedback I decide to keep it here. This article cannot be part of the Dirac equation

itself because of the potential to be expanded extensively. Three are only two formalisms of the Dirac equation using geometric algebra and both have the characteristic of being matrix free and therefore the standard approach can be considered only as an instance in some matrix representation Cabrer7 21:27, 6 November 2007 (UTC)[reply]

It's not at all clear why this isn't just an unusual way of writing Cl(3,1) algebra. And specifically to the Dirac equation, it's not clear what the math suggests about the physical theory. What good is a "matrix-free" formulation if you have to introduce an arbitrary spin axis? If you mean that a four-component Dirac spinor is only a projection of something larger (eight components, perhaps?), along an axis introduced by measurement, then say so. 107.77.194.190 (talk) 15:48, 2 October 2016 (UTC)Collin237[reply]

I've just found an essay by someone who independently discovered this "doubling problem" and found an interesting way to resolve it. https://arxiv.org/abs/math-ph/0201049 He suggests that the other four components can be a neutrino. Running further with this idea, could the spin axis be a W boson? 107.77.193.11 (talk) 16:21, 12 October 2016 (UTC)Collin237[reply]