On the Renormalization of Hamiltonians

TL;DR

This paper presents a new Wilson-inspired method for Hamiltonian renormalization in Quantum Field Theory, enabling effective low-energy Hamiltonians through unitary transformations, demonstrated on scalar b4 bb^4 theory.

Contribution

It introduces a novel unitary transformation approach for Hamiltonian renormalization, advancing the computation of effective low-energy Hamiltonians in QFT.

Findings

Successfully computed the 2-loop renormalized Hamiltonian in scalar b4 bb^4 theory.

Demonstrated the effectiveness of the method in decoupling high-frequency degrees of freedom.

Provided a new framework inspired by Wilson's renormalization group for Hamiltonian analysis.

Abstract

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 successively 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 $\lambda \phi^4$ theory.