Non-abelian gauge theories on non-commutative spaces

The construction of a non-abelian gauge theory on non-commutative spaces is based on enveloping algebra-valued gauge fields. The number of independent field components is reduced to the number of gauge fields in a usual gauge theory. This is done with the help of the Seiberg-Witten map. The dynamics is formulated with a Lagrangian where additional couplings appear.