Symplectic spinor bundle
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In differential geometry, given a metaplectic structure on a
-dimensional symplectic manifold
the symplectic spinor bundle is the Hilbert space bundle
associated to the metaplectic structure via the metaplectic representation. The metaplectic representation of the metaplectic group — the two-fold covering of the symplectic group — gives rise to an infinite rank vector bundle; this is the symplectic spinor construction due to Bertram Kostant.[1]
A section of the symplectic spinor bundle is called a symplectic spinor field.