All the derivations of the Schwinger-Dyson equation I can find are done using either the path integral formalism, or for the oldest papers, Schwinger's own quantum action principle formalism, which, while it resembles the Heisenberg formalism, assumes that the operator derived in the process is an operator version of the action.

Does there exist any derivation of the Schwinger-Dyson equations derived purely from regular matrix mechanics, using the Hamiltonian as its basis? I assume the trick might be to simply show that the Lagrangian operator used in the quantum action principle is $\approx \hat \pi {\partial_t \hat \phi} - \hat H$, but I have been unable to find any such derivation.

This post imported from StackExchange Physics at 2016-09-03 19:17 (UTC), posted by SE-user Slereah