Confinement interaction in nonlinear generalizations of the Wick-Cutkosky model

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 ${\varphi }^3+{\varphi }^4$ 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.

15 pages, 1 figure, LaTeX

References in corpus (1)

• Auxiliary fields as a tool for computing analytical solutions of the Schrödinger equation

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