{\displaystyle {\mathrm {Spin} }(n).} Clifford bundle Clifford module bundle Orthonormal frame bundle Spin geometry Spinor Spinor representation Friedrich, Thomas (2000)...

tensors, a spinor transforms to its negative when the space rotates through 360° (see picture). It takes a rotation of 720° for a spinor to go back to...

case of the Atiyah–Singer–Dirac operator acting on sections of a spinor bundle. For a spin manifold, M, the Atiyah–Singer–Dirac operator is locally defined...

a spin structure on an orientable Riemannian manifold (M, g) allows one to define associated spinor bundles, giving rise to the notion of a spinor in...

infinite rank vector bundle; this is the symplectic spinor construction due to Bertram Kostant. A section of the symplectic spinor bundle Q {\displaystyle...

variety of Projective pure spinors, or simple spinor variety, of dimension m(m + 1)/2. (Another description of the pure spinor variety is as OGr + ⁡ ( m...

section through that bundle. Coupled to the frame bundle is a second bundle, the spinor bundle. A section through the spinor bundle is just the particle...

corresponding to a given point group. Clifford algebra Clifford analysis Spinor Spinor bundle Spin structure Table of Lie groups Anyon Orientation entanglement Pin...

differential geometry and mathematical physics, a spin connection is a connection on a spinor bundle. It is induced, in a canonical manner, from the affine...

the spinor bundle, depending on the local choice of a coordinate frame. Put another way, a spinor field is a local section of the spinor bundle, and...

curvature, and results on spinors and spin structures. Given a spin structure on a pseudo-Riemannian manifold M and a spinor bundle S, the Lichnerowicz formula...

algebra on spinors. A spinor is said to be a pure spinor if it is annihilated by half of a set of generators of the Clifford algebra. Spinors are sections...

Hypercomplex number Octonion Paravector Quaternion Spin group Spin structure Spinor Spinor bundle Also known as a geometric algebra (especially over the...

a spinor bundle. In fact, on a Spin manifold, every Clifford module is obtained by twisting the spinor bundle. The notion "Clifford module bundle" should...

being an integrability condition so that the Frobenius theorem applies. Spinor bundle All of these constructions are due to Ehresmann (1941-3). Attributed...

geometry Symplectic topology Spinor Spinor bundle Spin manifold Lawson, H. Blaine; Michelsohn, Marie-Louise (1989). Spin Geometry. Princeton University Press...

bundle – Continuous surjection satisfying a local triviality condition Spinor bundle – Geometric structure Tensor field – Assignment of a tensor continuously...

quasinormal mode no-cloning theorem quantum entanglement spinor, spinor group, spinor bundle Dirac sea Spin foam Poincaré group gamma matrices Dirac adjoint Wigner's...

spin structure on orientable Riemannian manifolds. A metaplectic structure on a symplectic manifold allows one to define the symplectic spinor bundle...

Spin(4) on which U(1) acts by multiplication. We have K = c 1 ( W + ) = c 1 ( W − ) {\displaystyle K=c_{1}(W^{+})=c_{1}(W^{-})} . The spinor bundle W...

A} and spinor field ψ {\displaystyle \psi } . In this case the four-manifold must admit a SpinC structure, which defines a principal SpinC bundle P {\displaystyle...

In mathematics, and particularly topology, a fiber bundle (Commonwealth English: fibre bundle) is a space that is locally a product space, but globally...

of the (co)tangent bundle and a Weyl spinor bundle, the construction carries over to a differentiable manifold with a spinor bundle. The σ {\displaystyle...

a spinor is equivalent to the vanishing of the Lie derivative along the same Killing vector of all the spinor bi-linear quantities. While a spinor that...

In quantum field theory, the Dirac spinor is the spinor that describes all known fundamental particles that are fermions, with the possible exception of...

relates a four-component spinor to its charge conjugate. As a 2×2 differential equation acting on a complex two-component spinor, resembling the Weyl equation...

operators. Orthonormal frame bundle Spinor Spin manifold Spinor representation Spin geometry Spin structure Clifford module bundle Penrose, Roger (2004). The...

algebra Complex spin structure Conformal manifold Conformally flat manifold Dirac operator Poincaré metric Spin group Spin structure Spinor bundle Ahlfors, L...

pure spinor field. If M is a spin manifold, then Hol(ω) ⊂ SU(n) if and only if M admits at least two linearly independent parallel pure spinor fields...

is even if it is finite. Darboux theorem Symplectic frame bundle Symplectic spinor bundle Symplectic vector space Maurice de Gosson: Symplectic Geometry...