# nLab spin connection

### Context

#### Differential geometry

differential geometry

synthetic differential geometry

# Contents

## Idea

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.

## References

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