Quasi-invariant Utiyama’s approach to Chern—Simons’ theory

Abstract

We extend Utiyama’s approach to gauge theory by allowing the quasi-invariance of the Lagrangian density, that is the necessary and sufficient condition for the invariance of the action. Such an extension is possible because it is the invariance of the action, rather than the strict invariance of the Lagrangian density (that was the condition imposed by Utiyama), the condition that defines a symmetry. We obtain as a result that Chern—Simons’ theories, in the Abelian, non-Abelian, and gravity cases can be systematically obtained from the new set of Utiyama’s equations.