Geometric Properties of Quantum Phases

TL;DR

This paper explores the geometric nature of quantum phases, specifically the Aharonov-Anandan and Pancharatnam phases, using fiber bundle connections to provide a unified geometric framework.

Contribution

It introduces a geometric formulation of quantum phases via fiber bundle connections, offering new insights into their properties without relying on dynamical equations.

Findings

Aharonov-Anandan phase formulated geometrically

Pancharatnam phase derived through an alternative connection

Unified geometric framework for quantum phases

Abstract

The Aharonov-Anandan phase is introduced from a physical point of view. Without reference to any dynamical equation, this phase is formulated by defining an appropriate connection on a specific fibre bundle. The holonomy element gives the phase. By introducing another connection, the Pancharatnam phase formula is derived following a different procedure.