Construction of Local One-Parameter Subgroups Generated by the Virasoro Operators via Feynman Path Integrals

It is well known that the Virasoro algebra acts on the representations of an infinite-dimensional Heisenberg algebra, called the Fock models. We calculate Feynman path integrals on an coadjoint orbit of the infinite-dimensional Heisenberg group to give explicit formulae of actions of local one-parameters subgroups generated by the Virasoro operators.