The Geometric Phase and Ray Space Isometries
arXiv:quant-ph/9705019 · doi:10.1007/BF02847455
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.
17 pages, Latex file, no figures, To appear in Pramana J. Phys