Lorentz-Invariance and Gauge-Invariance of the Aharonov–bohm Phase

Abstract

We analyze general expressions for the quantum phases of dipoles and pointlike charges in an electromagnetic field, applying the strong relativistic limit and using the principle of superposition of quantum phases first proposed in Kholmetskii and Yarman (EPL 120: 40007, 2017). This way we derive a new expression for the AB phase of electrically charged particles, which is both gauge-invariant and Lorentz-invariant, and discuss its implications. © The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025.