Gauge group (mathematics)

In mathematical physics, a gauge group is the symmetry group ( gauge symmetry ) of a field theory. For non - commutative gauge groups these Yang-Mills theories are mentioned.

Definition

Let be a Lie group with Lie algebra, and is a principal bundle. The gauge group

Acts on the space of connections by

For.

Gauge groups are infinite-dimensional Lie groups, their Lie algebra is the vector space of differentiable maps from to.