2023/01/26 by Vivek M. Vyas, Vyas, Vivek M.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Optics (physics.optics) #Quantum Physics (quant-ph) #Quantum and Classical Electrodynamics #Quantum optics and atomic interactions #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2301.10929
openalex publication_date 2023/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A generalised notion of geometric phase for pure states is proposed and its physical manifestations are shown. An appreciation of fact that the interference phenomenon also manifests in the average of an observable, allows us to define the argument of the matrix element of an observable as a generalised relative phase. This identification naturally paves the way for defining an operator generalisation of the geometric phase following Pancharatnam. The notion of natural connection finds an appropriate operator generalisation, and the generalised geometric phase is indeed found to be the (an)holonomy of the generalised connection. It is shown that in scenarios wherein the usual geometric phase is not defined, the generalised geometric phase manifests as a global phase acquired by a quantum state in course of time evolution. The generalised geometric phase is found to contribute to the shift in the energy spectrum due perturbation, and to the forward scattering amplitude in a scattering problem.