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Geometric structure
In
differential geometry, given a
spin structure on an -dimensional orientable
Riemannian manifold one defines the spinor bundle to be the
complex vector bundle associated to the corresponding
principal bundle of spin frames over and the
spin representation of its
structure group on the space of
spinors .
A section of the spinor bundle is called a spinor field.
Formal definition
Let be a
spin structure on a
Riemannian manifold that is, an
equivariant lift of the oriented
orthonormal frame bundle with respect to the double covering of the
special orthogonal group by the
spin group.
The spinor bundle is defined
[1] to be the
complex vector bundle
associated to the
spin structure via the
spin representation where
denotes the
group of
unitary operators acting on a
Hilbert space It is worth noting that the spin representation
is a faithful and
unitary representation of the group
[2]
See also
Notes
Further reading
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Types of manifolds | |
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