spin connection

The term *spin connection* is traditionally used in physics – for instance in first-order formulation of gravity – to denote a connection on the tangent bundle of a manifold with spin structure given as a special orthogonal Lie algebra-valued connection on the underlying special orthogonal group-principal bundle. The term is mainly used to distinguish from the the connection expressed in Christoffel symbols. Since for this connection alone the spin structure is not important, the term *spin connection* is often used for $\mathfrak{so}$-connecition on any orientable manifold.

See at *field (physics)* the section *Ordinary gravity*.

Revised on January 6, 2013 08:11:04
by Urs Schreiber
(82.113.121.235)