Appearance of Gauge Structure in Simple Dynamical Systems

1984/06/11 by Frank Wilczek, A. Zee · 1 voice · 17 citations
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems #Topological Materials and Phenomena

paper · doi:10.1103/physrevlett.52.2111

openalex publication_date 1984/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

Generalizing a construction of Berry and Simon, we show that non-Abelian gauge fields arise in the adiabatic development of simple quantum mechanical systems. Characteristics of the gauge fields are related to energy splittings, which may be observable in real systems. Similar phenomena are found for suitable classical systems.

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Discussions

• The $(n\!+\!1)\times(n\!+\!1)$ matrix $T_{jk}\in so(n\!+\!1)$ is the Lie algebra generator of the rotation on the $jk$ plane in $\mathbb{R}^{n+1}$ , i.e. the $2\times 2$ submatrix formed by the $j$ th [stackexchange, 1 points]

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