Nonperturbative solution of scalar Yukawa model in two- and three-body Fock space truncations

TL;DR

This paper presents a detailed nonperturbative solution to the scalar Yukawa model using Light-Front Tamm-Dancoff method with Fock space truncations, including a sector-dependent renormalization scheme.

Contribution

It introduces a practical implementation of nonperturbative renormalization within Fock space truncations for the scalar Yukawa model, advancing nonperturbative field theory techniques.

Findings

Successful implementation of sector-dependent renormalization

Explicit solutions in two- and three-body Fock space truncations

Demonstration of the method's applicability to scalar Yukawa model

Abstract

The Light-Front Tamm-Dancoff method of finding the nonperturbative solutions in field theory is based on the Fock decomposition of the state vector, complemented with the sector-dependent nonperturbative renormalization scheme. We show in detail how to implement the renormalization procedure and to solve the simplest nontrivial example of the scalar Yukawa model in the two- and three-body Fock space truncations incorporating scalar "nucleon" and one or two scalar "pions".