Do you know what are the Hamiltonian formalism analogs of the Klein-Gordon equation and/or the Maxwell equations in general relativity?
Showing how these equations of motion for matter in the Hamiltonian formalism reproduce the known results from the Lagrangian formalism will be welcome.
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$\begingroup$ You are invited to compute them. $\endgroup$ – DanielC Dec 27 '18 at 15:48