Talk:Spin structure

From Wikipedia, the free encyclopedia

Mathematics Portal This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating:	Start Class	Low Priority	Field: Geometry
Please update this rating as the article progresses, or if the rating is inaccurate. Please also add comments to suggest improvements to the article.

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)

I also think it could use breaking off. The section on spin^c structures should probably be considered a fragment and in need of development. How vague can you get? "A spinc structure is analogous, but uses the spinc group, which is the U(1)-extension of SO(n) built on top of the extension by the cyclic group of order 2 in Spin(n)." What analogy are you using? Which U(1) extension are you talking about? etc. It's too vague. And there are no references. None of the references in this article mention spin^c structures. Rybu

Well, I found references at least for the definition of spin^c structures. I put in a proper definition (which should really be polished) and mentioned some of the most basic facts. I appended the Gompf reference. It's certainly not the original reference for the concept, but it was one of the easiest ones to find on-line. Who originated the notion of spin^c ? Rybu —Preceding signed but undated comment was added at 04:05, 12 October 2007 (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)