Gauge fixing and constrained dynamics
Theory Group and Center for Gravitational Physics, University of Texas at Austin, 78712, Austin, TX, USA
Accepted: 3 December 2021
Published online: 19 December 2021
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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021