Inter-particle potentials in a scalar QFT with a Higgs-like mediating field

TL;DR

This paper investigates how non-linear Higgs-like mediating fields affect inter-particle potentials in scalar quantum field theory, revealing modifications to Yukawa potentials while maintaining their attractive nature.

Contribution

It introduces a variational approach within a reformulated Hamiltonian framework to derive relativistic multi-particle wave equations with non-linear mediating fields.

Findings

Non-linear terms modify Yukawa potentials

Attractive nature persists with massive mediating fields

Relativistic multi-particle wave equations derived

Abstract

We study the inter-particle potentials for few-particle systems in a scalar theory with a non-linear mediating field of the Higgs type. We use the variational method, in a reformulated Hamiltonian formalism of QFT, to derive relativistic three and four particle wave equations for stationary states of these systems. We show that the cubic and quartic non-linear terms modify the attractive Yukawa potentials but do not change the attractive nature of the interaction if the mediating fields are massive.