The Geometric Phase and Ray Space Isometries

Details The Geometric Phase and Ray Space Isometries The Geometric Phase and Ray Space Isometries

1997-05-12

arxiv.org/abs/quant-ph/9705019v1

Physics

Quantum Physics

17 pages, Latex file, no figures, To appear in Pramana J. Phys

Scientific paper

10.1007/BF02847455

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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