Berry phases for partial cycles

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Abstract
A simple definition of Berry phases based on the Pancharatnam phase convention is stated in the language of ordinary quantum mechanics. It is shown to be equivalent to previous definitions for a cycle of transformations built continuously from infinitesimal transformations. It also applies to discrete transformations and partial cycles. The phase for a partial cycle can be the same as for the complete cycle. This suggests possibilities for simpler experiments. In an example considered here, each part of a split beam of light is put through two half-wave plates. The light is not brought back to the original polarization state, but interference produced by the Berry phase can be observed because the different parts of the beam are brought to the same polarization state.

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