Spinor field

In differential geometry, given a spin structure on a n-dimensional Riemannian manifold (M, g) a section of the spinor bundle S is called a spinor field. The complex vector bundle

is associated to the corresponding principal bundle

of spin frames over M via the spin representation of its structure group Spin(n) on the space of spinors Δ_n.

In particle physics particles with spin s are described by 2s-dimensional spinor field, where s is an integer or a half-integer. Fermions are described by spinor field, while bosons by tensor field.

Let (P, F_P) be a spin structure on a Riemannian manifold (M, g) that is, an equivariant lift of the oriented orthonormal frame bundle ${\displaystyle \mathrm {F} _{SO}(M)\to M}$ with respect to the double covering ${\displaystyle \rho :{\mathrm {Spin} }(n)\to {\mathrm {SO} }(n)\,.}$

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