Construction of conserved covariant current operators in phenomenological relativistic quantum models of strongly interacting systems.

I discuss a systematic method for constructing conserved covariant current operators that are consistent with the dynamics in phenomenological relativistic models of strongly interacting systems. The current is constructed by expressing the Hamiltonian in the Weyl representation, replacing the momentum operators by gauge covariant derivatives, and extracting the coefficient of the part of the operator that is linear in vector potential. The method generates the representation-dependent many-body parts of the current operator that are needed in order to satsify the dynamical constraints of current covaraince and current conservation. Because the resulting current is an operator, it can be consistently applied to different reactions. Non-commuting operators are treated explicitly using Trotter methods.