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arXiv · quant-ph/9705019

The Geometric Phase and Ray Space Isometries

Joseph Samuel
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Abstract

We study the behaviour of the geometric phase under isometries of the ray space. This leads to a better understanding of a theorem first proved by Wigner: isometries of the ray space can always be realised as projections of unitary or anti-unitary transformations on the Hilbert space. We suggest that the construction involved in Wigner's proof is best viewed as an use of the Pancharatnam connection to ``lift'' a ray space isometry to the Hilbert space.

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Joseph Samuel. 1997-05-12. The Geometric Phase and Ray Space Isometries. https://doi.org/10.1007/bf02847455

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