Electric Charge Quantization

Abstract

Experimentally it has been known for a long time that the electric charges of the observed particles appear to be quantized. An approach to understanding electric charge quantization that can be used for gauge theories with explicit $U(1)$ factors -- such as the standard model and its variants -- is pedagogically reviewed and discussed in this article. This approach uses the allowed invariances of the Lagrangian and their associated anomaly cancellation equations. We demonstrate that charge may be de-quantized in the three-generation standard model with massless neutrinos, because differences in family-lepton--numbers are anomaly-free. We also review the relevant experimental limits. Our approach to charge quantization suggests that the minimal standard model should be extended so that family-lepton--number differences are explicitly broken. We briefly discuss some candidate extensions (e.g. the minimal standard model augmented by Majorana right-handed neutrinos).