Talk:Spin structure

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I'm thinking of breaking off spin^c structure into a separate article. After all, it's longer than the section on the spin structure itself, which isn't so strange as it's more complicated/interesting (although there's a lot that one could add to the spin structure section about applications various theories (and exotic stuff like supersymmetry without supersymmetry) and one could talk about various properties of spin manifolds, like the canonical division by two of the first Pontrjagin class which gives Witten's characteristic class, etc ... although I don't know if I know enough about any of these topics to include them myself). Any comments/objections? JarahE 19:41, 24 April 2006 (UTC)

[edit] This seemed out of place

I removed the following paragraph, since it certainly didn't belong in the intro, and it may not even belong in the article at all:

In particle physics the spin statistics theorem implies that the wavefunction of an uncharged fermion is a section an associated vector bundle to a the spin lift of an SO(N) bundle E. Therefore the choice of spin structure is part of the data needed to define the wavefunction, and often needs to be summed over in the partition function. In many physical theories E is the tangent bundle, but for the fermions on the worldvolumes of D-branes in string theory it is the normal bundle.

Silly rabbit 19:55, 21 June 2006 (UTC)

Spin structures are important in particle physics. Particle physics in turn was crucial to the history of spin structures, the name term "spin structure" itself I think owes its origins to particle physics. So the connection between the two I think needs to appear in the article, if not in the introduction, although I agree that the above paragraph is too technical for an introduction. Perhaps a compromise would be a nontechnical sentence in the introduction and then the above paragraph can be put in a particle physics subsection analogous to that in the spin^c section. --JarahE 07:35, 2 July 2006 (UTC)

Fair enough. Shall we create a Spin structures in particle physics section (or such-like), and point it out in the intro? Silly rabbit 19:12, 2 July 2006 (UTC)

I vote to keep Spin-c here. Morally, these are just another "kind" of "spin" structures (a propos of spinors). Silly rabbit 21:36, 2 July 2006 (UTC)

Ok, so then maybe we should put in a redirect so that people searching for spin^c structures get here? I'm not sure how to do this with the superscript, maybe redirect all of the various ways that people could try to type it? JarahE 12:02, 3 July 2006 (UTC)

[edit] Application to particle physics

In section 2.3, the first two sentences seem garbled - I'll underline what I think is weird. Can someone who knows fix them?

In particle physics the spin statistics theorem implies that the wavefunction of an uncharged fermion is a section an associated vector bundle to a the spin lift of an SO(N) bundle E. Therefore the choice of spin structure is part of the data needed to define the wavefunction, and often needs to be summed over in the partition function.

Orthografer 18:31, 5 September 2006 (UTC)