Poincaré gauge symmetries, Hamiltonian symmetries, and trivial gauge transformations

We resolve a problem of finding the Poincaré symmetries from Hamiltonian gauge symmetries constructed through a canonical procedure of handling constrained systems. Through the use of Noether identities corresponding to the symmetries, we motivate a procedure of finding the map between the Hamiltonian and Poincaré gauge parameters. Using this map, we show that the Poincaré and Hamiltonian gauge symmetries are equivalent, modulo trivial gauge transformations.