Renormalization by projection: on the equivalence of the Bloch-Feshbach formalism and Wilsonʹs renormalization

We employ projection operator techniques in Hilbert space to derive a continuous sequence of effective Hamiltonians which describe the dynamics on successively larger length scales. We show for the case of φ4 theory that the masses and couplings in these effective Hamiltonians vary in accordance with 1-loop renormalization group equations. This is evidence for an intimate connection between Wilsonʹs renormalization and the venerable Bloch-Feshbach formalism.