Related papers: Generalised Geometric Phase: Mathematical Aspects

Generalised Geometric Phase: Mathematical Aspects

URL: http://arxiv.org/abs/2312.14522v1
Date: Fri, 22 Dec 2023 08:42:11 GMT
Title: Generalised Geometric Phase: Mathematical Aspects
Authors: Vivek M. Vyas
Abstract summary: An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. We provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum systems.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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.

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