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

TL;DR

This paper demonstrates that the Bloch-Feshbach formalism is fundamentally equivalent to Wilson's renormalization group approach by deriving effective Hamiltonians that follow 1-loop RG equations in b4^4 theory.

Contribution

It establishes a formal connection between projection operator techniques and Wilson's renormalization, showing their equivalence in deriving effective Hamiltonians.

Findings

Effective Hamiltonians follow 1-loop RG equations.

Bloch-Feshbach formalism is equivalent to Wilson's renormalization.

Provides a unified perspective on renormalization methods.

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 \phi^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.