Spinors | Differential geometry | Connection (mathematics)

Spin connection

In 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 connection. It can also be regarded as the gauge field generated by local Lorentz transformations. In some canonical formulations of general relativity, a spin connection is defined on spatial slices and can also be regarded as the gauge field generated by local rotations. The spin connection occurs in two common forms: the Levi-Civita spin connection, when it is derived from the Levi-Civita connection, and the affine spin connection, when it is obtained from the affine connection. The difference between the two of these is that the Levi-Civita connection is by definition the unique torsion-free connection, whereas the affine connection (and so the affine spin connection) may contain torsion. (Wikipedia).

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Contorsion tensor | Lie group | Curvature form | Differential form | Fiber bundle | Connection (vector bundle) | Spinor bundle | Gauge theory gravity | Lorentz group | General covariance | Spinor | Dirac equation | Riemann curvature tensor | Levi-Civita connection | Riemannian geometry | Cotangent bundle | Dirac equation in curved spacetime | Christoffel symbols | Dirac operator | Cartan connection | Connection form | Ricci calculus | Torsion tensor | Curvature | Differential geometry | Homogeneous space | Einstein–Hilbert action | Supergravity | Affine connection