Yang-Mills theory is a gauge theory of connections 
on a principal
bundle with Lie group 
over a Riemannian manifold 
. The connection has bundle
curvature 
.
Given an invariant inner product on the Lie
algebra of 
,
the Yang-Mills functional is
 |
Its critical points satisfy the Yang-Mills equation 
.
In four dimensions, self-dual and anti-self-dual connections
give important applications of Yang-Mills theory
to the topology of manifolds.
