Journal of Physical Studies 15(1), Article 1101 [9 pages] (2011)
DOI: https://doi.org/10.30970/jps.15.1101

ON CONFINEMENT INTERACTIONS IN SCALAR GENERALIZATIONS OF THE DIPOLE MODEL

A. Duviryak¹, J. W. Darewych²
¹Department for Computer Simulations of Many-Particle Systems,
Institute for Condensed Matter Physics of NAS of Ukraine,
1, Svientsitskii St., Lviv, UA--79011, Ukraine,
²Department of Physics and Astronomy, York University,
4700, Keele St., Toronto, Ontario, M3J 1P3, Canada

Two modified versions of the dipole model with a pair of mediating fields are considered. In the first version, the modification affects the Yukawa term in the Lagrangian. In the second version a non-linear self-action term is added. By constructing exact solutions of the field equations with the use of a covariant Green function we derive a Lagrangian with many-point time-nonlocal interaction terms. For the linear dipole model the two-particle interaction, in the non-relativistic limit, is shown to be a sum of Coulomb and linear confinement terms. For the nonlinear $φ^3$-model the interactions are shown to include pairwise potentials and also three-particle cluster potentials with a logarithmic confinement. The approaches towards a consistent relativistic treatment of the models are proposed, and the problem of divergences is discussed.

PACS number(s): 11.10.Ef, 11.10.Lm