A BBGKY-like Heirachy for Quantum Field Theories

We present a general method for constructing BBGKY-like hierarchies of arbitrary quantum field theories. Further, we show that our hierarchy has a natural Hamiltonian structure directly analogous to the classical case. Under suitable choices, we show how our method creates a system of BBGKY-like evolution equations for the k-th order reduced density matrices. These equations can be closed at finite order to give non-perturbative, semi-classical, and structure-preserving approximation schemes for quantum field theories, particularly quantum electrodynamics.