Nonadiabatic geometric phase in quaternionic Hilbert space

1996/09/30 by Stephen L. Adler, J. Anandan, Jeeva Anandan · 5 citations
Mathematics · Physics and Astronomy · #Abelian group #Algebraic and Geometric Analysis #Computer science #Geometric phase #Hilbert space #Mathematical analysis #Mathematics #Phase (matter) #Phase space #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Space (punctuation) #Spectral Theory in Mathematical Physics #hep-th

paper · pdf · doi:10.1007/bf02282121

published in Foundations of Physics 26(12), 1579-1589 (Springer Science+Business Media) · 14 pages, plain Tex, no figures

arxiv created 1996/09/30 · openalex publication_date 1996/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space.

Citations

• Appearance of Gauge Structure in Simple Dynamical Systems
• Quantal phase factors accompanying adiabatic changes

Cited by

• Lattice gauge fields topology uncovered by quaternionicσ-model embedding
• Correlation-induced non-Abelian quantum holonomies