  We outline a procedure for applying Hamiltonian Truncation to Quantum Field
Theories (QFTs) that have UV divergences. To do this, we derive a novel
representation of an Effective Hamiltonian which makes manifest some of its
important properties (e.g. the non-perturbative matching of the spectra between
the UV theory and the theory described by the Effective Hamiltonian). We check
the consistency of our procedure using Conformal Perturbation Theory. Finally
we comment on how the Effective Hamiltonian, which incorporates non-local
interactions, describes a local QFT.
