Noncyclic geometric phase and its non-Abelian generalization

1999/09/30 by Ali Mostafazadeh · 4 citations
Mathematics · Physics and Astronomy · #Abelian group #Adiabatic process #Gauge theory #Generalization #Geometric phase #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum Mechanics and Applications #Quantum and Classical Electrodynamics #Quantum chaos and dynamical systems #Quantum mechanics #Theoretical physics #hep-th #quant-ph

paper · pdf · doi:10.1088/0305-4470/32/46/312

published as J.Phys.A32:8157-8171,1999 · Plain Latex, accepted for publication in J. Phys. A: Math. Gen

arxiv created 1999/09/30 · openalex publication_date 1999/11/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We use the theory of dynamical invariants to yield a simple derivation of noncyclic analogues of the Abelian and non-Abelian geometric phases. This derivation relies only on the principle of gauge invariance and elucidates the existing definitions of the Abelian noncyclic geometric phase. We also discuss the adiabatic limit of the noncyclic geometric phase and compute the adiabatic non-Abelian noncyclic geometric phase for a spin-1 magnetic (or electric) quadrupole interacting with a precessing magnetic (electric) field.

Citations

• Geometry, Topology and Physics
• Quantum adiabatic approximation and the geometric phase
• Topological Aspects of the Non-adiabatic Berry Phase
• Appearance of Gauge Structure in Simple Dynamical Systems
• Quantal phase factors accompanying adiabatic changes

Cited by

• Perturbative calculation of the adiabatic geometric phase and particle in a well with moving walls
• Vacuum Condensate, Geometric Phase, Unruh Effect, and Temperature Measurement
• On the dynamical invariants and the geometric phases for a general spin system in a changing magnetic field
• Noncyclic and nonadiabatic geometric phase for counting statistics