Is the geometric phase unique?

In this talk we shall briefly review the concept of geometric phase following the trail of Pancharatnam. Subsequently we shall see that the notion of geometric phase so defined is not unique, and there exists a natural operator generalisation of this notion. It will be shown that in scenarios wherein the usual geometric phase is not defined, the generalised geometric phase manifests as a global phase acquired by a quantum state in course of time evolution. The underlying mathematical structure giving rise to this geometric phase will also be discussed.