Deciphering Pancharatnam's discovery of geometric phase

Abstract: While Pancharatnam discovered the geometric phase in 1956, his work was not widely recognized until its endorsement by Berry in 1987, after which it received wide appreciation. However, because Pancharatnam's paper is unusually difficult to follow, his work has often been misinterpreted as referring to an evolution of states of polarization, just as Berry's work focused on a cycle of states, even though this consideration does not appear in Pancharatnam's work. We walk the reader through Pancharatnam's original derivation and show how Pancharatnam's approach connects to recent work in geometric phase. It is our hope to make this widely cited classic paper more accessible and better understood.