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The geometric phase and ray space isometries

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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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Authors and Affiliations

  1. Raman Research Institute, 560 080, Bangalore, India

    Joseph Samuel

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  1. Joseph Samuel
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Samuel, J. The geometric phase and ray space isometries. Pramana - J Phys 48, 959–967 (1997). https://doi.org/10.1007/BF02847455

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  • DOI: https://doi.org/10.1007/BF02847455

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