2023/12/22 by Vivek M. Vyas, Vyas, Vivek M.
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Geometry and complex manifolds #Nonlinear Waves and Solitons #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2312.14522
openalex publication_date 2023/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum systems. While probing the average of any observable it is found that a quantum system exhibits different ray spaces and associated fibre bundle structures. The generalised geometric phase is understood as (an)holonomy of a connection over these fibre bundles. The underlying ray spaces in general are found to be pseudo-Kahler manifolds, and its symplectic structure gets manifests as the generalised geometric phase.