Null Phase Curves and Manifolds in Geometric Phase Theory

TL;DR

This paper explores the geometric and symplectic structures of null phase manifolds in quantum ray spaces, providing a comprehensive characterization crucial for understanding geometric phases in quantum mechanics.

Contribution

It offers a novel complete characterization of null phase manifolds by integrating Riemannian and symplectic structures, advancing the geometric phase theory.

Findings

Null phase manifolds are characterized by both metric and symplectic structures.

The work unifies geometric and symplectic approaches in quantum phase analysis.

Provides insights into the structure of quantum ray spaces and phase phenomena.

Abstract

Bargmann invariants and null phase curves are known to be important ingredients in understanding the essential nature of the geometric phase in quantum mechanics. Null phase manifolds in quantum-mechanical ray spaces are submanifolds made up entirely of null phase curves, and so are equally important for geometric phase considerations. It is shown that the complete characterization of null phase manifolds involves both the Riemannian metric structure and the symplectic structure of ray space in equal measure, which thus brings together these two aspects in a natural manner.