A Construction of an Effective Hamiltonian from Feynman Diagrams: Application to the Light-Front Yukawa Model

TL;DR

This paper presents a systematic method to construct an effective Hamiltonian from Feynman diagrams for the Light-Front Yukawa model, simplifying calculations and ensuring proper renormalization.

Contribution

It introduces a new set of rules for deriving an effective Hamiltonian directly from Feynman diagrams, applicable to the Light-Front Yukawa model, with proven renormalization.

Findings

Effective Hamiltonian constructed from Feynman diagrams

Renormalization achieved via covariant perturbation theory

Numerical diagonalization performed to second order

Abstract

We study a similarity transformation to construct an effective Hamiltonian systematically, which does not contain particle-number-changing interactions, by means of Fukuda-Sawada-Taketani-Okubo's method. We show that such Hamiltonian can be constructed from Feynman diagrams and give rules for constructing it in the Light-Front Yukawa model. We prove that it is renormalized by the familiar covariant perturbative renormalization procedure. It is very advantageous that the effective Hamiltonian can be obtained from our rules {\em immediately}. We also numerically diagonalize it to the second order in the coupling constant as an exercise.