Renormalization by Projection: On the Equivalence of the Bloch-Feshbach Formalism and Wilson's Renormalization

Abstract

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 ϕ^4 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 Wilson's renormalization and the venerable Bloch-Feshbach formalism.

8 pages LaTeX, no figures; revised introduction and discussion, new title

References in corpus (3)

• From Quantum Field Theory to Hydrodynamics: Transport Coefficients and Effective Kinetic Theory
• From Reversible Quantum Microdynamics to Irreversible Quantum Transport
• Exact Solutions of Model Hamiltonian Problems with Effective Interactions

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• Renormalization Group Transformation for the Wave Function
• Transport theory yields renormalization group equations