In differential geometry, given a metaplectic structure π P : P → M {\displaystyle \pi _{\mathbf {P} }\colon {\mathbf {P} }\to M\,} on a 2 n {\displaystyle 2n} -dimensional symplectic manifold, {\displaystyle,\,} the symplectic spinor bundle is the Hilbert space bundle π Q : Q → M {\displaystyle \pi _{\mathbf {Q} }\colon {\mathbf {Q} }\to M\,} associated to the metaplectic structure via the metaplectic representation. Wikipedia