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Confinement interaction in nonlinear generalizations of the Wick-Cutkosky model
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
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.Comment: 15 pages, 1 figure, LaTe