Confinement interaction in nonlinear generalizations of the Wick-Cutkosky model

TL;DR

This paper explores nonlinear generalizations of the Wick-Cutkosky model, deriving a confining three-current interaction and a relativistic three-particle wave equation, advancing understanding of confinement in quantum field theories.

Contribution

It introduces a new nonlinear mediating field approach, deriving a confining interaction and a relativistic three-particle wave equation with a variational method.

Findings

Derivation of a confining three-current interaction.

Development of a relativistic three-particle wave equation.

Analysis of the non-relativistic limit and properties.

Abstract

We consider nonlinear-mediating-field generalizations of the Wick-Cutkosky model. Using an iterative approach and eliminating the mediating field by means of the covariant Green function we arrive at a Lagrangian density containing many-point time-nonlocal interaction terms. In low-order approximations of $\phi^3{+}\phi^4$ theory we obtain the usual two-current interaction as well as a three-current interaction of a confining type. The same result is obtained without approximation for a version of the dipole model. The transition to the Hamiltonian formalism and subsequent canonical quantization is performed with time non-locality taken into account approximately. A relativistic three-particle wave equation is derived variationally by using a three-particle Fock space trial state. The non-relativistic limit of this equation is obtained and its properties are analyzed and discussed.