The Geometric Phase and Ray Space Isometries
Quantum Physics
2009-10-30 v1
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.
Cite
@article{arxiv.quant-ph/9705019,
title = {The Geometric Phase and Ray Space Isometries},
author = {Joseph Samuel},
journal= {arXiv preprint arXiv:quant-ph/9705019},
year = {2009}
}
Comments
17 pages, Latex file, no figures, To appear in Pramana J. Phys