On the Renormalization of Hamiltonians

We introduce a novel method for the renormalization of the Hamiltonian operator in Quantum Field Theory in the spirit of the Wilson renormalization group. By a series of unitary transformations that suc-cessively decouples the high-frequency degrees of freedom and partially diagonalizes the high-energy part, we obtain the effective Hamiltonian for the low energy degrees of freedom. We successfully apply this technique to compute the 2-loop renormalized Hamiltonian in scalar λ φ 4 theory.