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Results tagged with spin-geometry
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user 394
For questions about spin manifolds, the groups $\operatorname{Spin}(n)$, as well as generalisations such as $\operatorname{Pin}^{\pm}(n)$ and $\operatorname{Spin}^c(n)$. This tag should also be used for any questions about the geometry of spin manifolds, including questions involving Dirac operators and the Lichnerowicz formula.
4
votes
Accepted
Twistors for spaces of $n-$dimensions
"Twistors are spinors of the compactified Minkowski space" is not
quite true. Twistors in Minkowski space are spinor fields which
satisfy a particular PDE: the twistor spinor equation. Relative to
f …
- 33.3k
5
votes
equivariant index of Dirac Operator on $S^{2}$
There are many questions here. I can answer the first one quickly: there are no harmonic spinors on $S^2$ with the standard round metric. This follows from Lichnerowicz theorem. A good place to rea …
- 33.3k
5
votes
Explicit Spin Structures on the Torus
Why are you after representations of $\mathrm{SU}(2)$? Since you are looking at a two-dimensional spin manifold, the spinor bundles have structure group $\mathrm{Spin}(2)$, which is the double cover …
- 33.3k
7
votes
Conformal Killing spinors
(By the way, the use of "holomorphic" and "antiholomorphic" is wrong in your question. This may be confusing people, which perhaps explains why nobody has answered this question yet.)
Conformal Killi …
- 33.3k
11
votes
Exact Definition of Dirac Operator
Let $(M,g)$ be an orientable pseudo-riemannian manifold. Each tangent space $T_xM$ is a pseudo-euclidean space and hence has an associated Clifford algebra $CL(T_xM)$, which is the fibre at $x\in M$ …
- 33.3k