Comment on "Gauge Symmetries and Dirac Conjecture" by Y.-L. Wang, Z.-P. Li, K. Wang and some other counterexamples to the Dirac conjecture

TL;DR

This paper critiques a previous claim that the Dirac conjecture is invalid, arguing that the analysis was flawed and clarifying the gauge symmetry in Maxwell theory and a classical counterexample.

Contribution

It provides a critical reassessment of prior counterexamples to the Dirac conjecture, correcting the analysis and clarifying gauge symmetries in classical theories.

Findings

The previous analysis of the Maxwell theory's gauge symmetry was flawed.

The paper clarifies the correct interpretation of the Allcock counterexample.

It demonstrates the importance of proper analysis in assessing the Dirac conjecture.

Abstract

We argue that the conclusion about the invalidity of the Dirac conjecture, made in the paper by Wang, Li, and Wang (Int. J. Theor. Phys. 48 1894, 2009), was based upon a flawed analysis of the proposed counterexamples. In the case of the Maxwell theory, the well-known gauge symmetry is contradicted by the results in the Hamiltonian and Lagrangian approaches presented by the authors. We also consider the oldest counterexample to the Dirac conjecture due to Allcock and present its natural parametrization.