Abstract
We review the Dirac formalism for dealing with constraints in a canonical Hamiltonian formulation, discuss gauge freedom, and display constraints for gauge theories in a general context. We introduce the Dirac bracket and show that it provides a consistent method to remove any gauge freedom present. We discuss stability in evolution of gauge theories and show that fixing all gauge freedom is sufficient to ensure well-posedness for a large class of gauge theories. Electrodynamics provides examples of the methods outlined for general gauge theories. Future work will apply the formalism, and results derived here, to General Relativity.
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Acknowledgements
We thank Claudio Bunster, Mark Henneaux, David Brown, and Phil Morrison for their interesting early discussion.
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Allen, J., Matzner, R.A. Gauge fixing and constrained dynamics. Eur. Phys. J. Plus 137, 41 (2022). https://doi.org/10.1140/epjp/s13360-021-02258-2
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DOI: https://doi.org/10.1140/epjp/s13360-021-02258-2