Spinor bundle |
Given a differentiable manifold M with a Cartan connection applications of metric signature ( p , q ) over it, a spinor bundle over M is a vector bundle over M such that its fiber bundle is a spinor representations of Lie groups/algebras of
: Spin ( p , q ),
the double cover of the special orthogonal group SO ( p , q ).
Spinor bundles inherit a connection (vector bundle) from a connection on the vector bundle V (see Cartan connection applications).
When
: p + q ≤ 3
there are some further possibilities for covering groups of the orthogonal group, so other fiber bundle (anyonic bundles).
See also associated bundle.|
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