Confinement interaction in nonlinear generalizations of the Wick-Cutkosky model

Details Confinement interaction in nonlinear generalizations of the Wick-Cutkosky model Confinement interaction in nonlinear generalizations of the Wick-Cutkosky model

2009-10-23

arxiv.org/abs/0910.4552v2

J.Phys.A43:485402,2010

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, 1 figure, LaTeX

Scientific paper

10.1088/1751-8113/43/48/485402

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.

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