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

Understand

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.