Spin connection

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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 Levi-Civita connection.

[edit] Definition

\omega^{ab}_{\mu} is the spin connection:

\omega_{\mu}^{ab} = e^a_\nu \partial_\mu e^{\nu b} + e^a_\nu e^{\sigma b} \Gamma^\nu_{\sigma\mu}

where \Gamma^\nu_{\sigma\mu} is the Christoffel symbol and the e^a_\nu are the local Lorentz frame fields or vierbein. Note that here, Latin letters denote the local Lorentz frame indices; Greek indices denote general coordinate indices.

[edit] See also

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