Geometric phases without geometry

TL;DR

This paper presents a straightforward quantum mechanical method to calculate geometric phases using energy level shifts, avoiding complex topological approaches, thereby simplifying analysis in various physical contexts.

Contribution

It introduces a new approach to compute geometric phases through standard energy shift calculations, bypassing the need for topological methods.

Findings

Method simplifies geometric phase calculations

Connects geometric phases to energy level shifts

Enables understanding of geometric phases without topology

Abstract

Geometric phases arise in a number of physical situations and often lead to systematic shifts in frequencies or phases measured in precision experiments. We describe, by working through some simple examples, a method to calculate geometric phases that relies only on standard quantum mechanical calculations of energy level shifts. This connection between geometric phases and off-resonant energy shifts simplifies calculation of the effect in certain situations. More generally, it also provides a way to understand and calculate geometric phases without recourse to topology.