Interparticle potentials in a scalar quantum field theory with a Higgs-like mediating field

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.

Particle–antiparticle potential in scalar quantum field theory with a Higgs-like mediating field

“…In a previous paper [1], we studied three-and four-particle bound-state systems in a model quantum field theory (QFT) in which scalar particles described by the field interact via exchange of quanta of a nonlinear Higgs-like scalar field, . The Lagrangian density of this model (in units of ប = c = 1) is…”

“…The term is usually added to Lagrangian density (1) to ensure that the classical ground state energy is bounded from below [2,3]. The terms lead to a contact interparticle interaction that is irrelevant for our purposes.…”

“…14.1). Indeed (1) can be thought of as a naive scalar mimic of QCD, in which the mass-m spin-1/2 colour quark field is replaced by the mass-m spin-0 colourless field, and the massless spin-1 gluon field is replaced by the massless ( = 0) spinless field. Note that if the coupling constants = = 0 then (1) is just the well-known scalar Yukawa model (see, e.g., ref.…”

“…We recall [1] that upon completion of the reformulation, the Hamiltonian density takes on the following form:…”

“…We proceed, initially, as in the previous paper [1], that is, we use the formal solution of the classical mediating-field equation of motion (i.e., the integral form of the equations), namely…”