1999/07/26 by Eqab M. Rabei, Arvind, Arvind Arvind +3 · 1 citation
Physics and Astronomy · #Crystallography and Radiation Phenomena #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #quant-ph
paper · pdf · doi:10.1103/physreva.60.3397
published as Phys.Rev.A60:3397,1999 · Accepted for publication in Physical Review A
arxiv created 1999/07/26 · openalex publication_date 1999/11/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We develop the broadest possible generalization of the well known connection between quantum-mechanical Bargmann invariants and geometric phases. The key concept is that of null phase curves in quantum-mechanical ray and Hilbert spaces. Examples of such curves are developed. Our generalization is shown to be essential for properly understanding geometric phase results in the cases of coherent states and of Gaussian states. Differential geometric aspects of null phase curves are also briefly explored.