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Questions tagged [spin-geometry]

For questions about spin manifolds, the groups $\operatorname{Spin}(n)$, as well as generalisations such as $\operatorname{Pin}(n)$ 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.

For questions about spin manifolds, the groups $\operatorname{Spin}(n)$, as well as generalisations such as $\operatorname{Pin}(n)$ 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.

334 questions
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Are spinors in 3 dimension quaternions, or are they elements of $\mathbb C^2$?

In Wikipedia both statement is present, which one is true? In one hand, here stands: def 1. Thus the (real) spinors in three-dimensions are quaternions, and the action of an even-graded element on a spinor is given by ordinary quaternionic…
mma
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some questions on spin group

The spin group of an inner product space $V$ is defined in terms of the Clifford algebra of $V$, which is spanned by products of vectors in $V$. Does any vector in $V$ correspond to a reflection in the normal sense? How can we explain …
Hao Yu
2
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1 answer

Existence of Harmonic Spinors

The harmonic spinor equation states that $D \psi=0$, where $D$ is a Dirac operator and $\psi$ is a spinor. A spinor satisfying this equation is said to be harmonic. Is there some result that one always define a harmonic spinor on a spin manifold…
Tom
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how to show all spin groups are double covers?

If that's the definition, then how do we know double covers of $SO(n)$ exist?
Alex
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Is there a geometrical interpretation of a spinor?

To give a geometrical interpretation of a vector one can associate a vector with two points in space $(A,B)$. Any vector can be thought of as an equivalence class of pairs of points. Like wise a symmetric 2-tensor can be thought of in terms of a…
zooby
  • 4,343
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Can somebody show an explicit example of a spinor?

I've seen a lot of articles of spinors defined using representation theory, Clifford Algebras, etc. But i want to see (if its possible) how a spinor "looks like" and how it changes sign with a 2pi rotation or any aplication.
Julian Ar.
  • 187