Integration by parts for heat measures over loop groups

The formula of integration by parts for heat measures over a loop group established by B. Driver is revesited through an alternative approach to this result. We shall first establish directly the integration by parts formula over an unimodular Lie group (which will be the finite product of a compact Lie group with a correlated metric), using the concept of tangent processes. A new expression for Ricci tensor will enable us the passage to the limit.