In mid-1950s, Pancharatnam  encountered the geometric phase associated with the evolution along a geodesic triangle on the Poincaré sphere. We generalize his 3-vertex phase and employ it as the fundamental building block, to geometrically construct a general ray-space expression for geometric phase. In terms of a reference ray used to specify geometric phase, we delineate clear geometric meanings for gauge transformations and gauge freedom, which are generally regarded as mere mathematical abstractions.
Volume 94, 2020
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