Differential geometry on SU(N): Left and right invariant vector fields and one-forms

Abstract

In this paper we provide an analytical procedure for explicit calculation of the left and right invariant vector fields and one-forms on SU(N) manifold. The calculations are based on the coset parametrization of SU(N) group. The results enable us to calculate the invariant measure or Haar measure on the group. As an illustrative example, we calculate invariant vector fields and one-forms on SU(2) group.