POSSIBLE CONFINEMENT MECHANISMS FOR NONRELATIVISTIC PARTICLES ON A LINE

Abstract

The gauge model of nonrelativistic particles on a line interacting with nonstandard gravitational fields5 is supplemented by the addition of a (non)-Abelian gauge interaction. Solving for the gauge fields we obtain equations, in closed form, for a classical two-particle system. The corresponding Schrödinger equation, obtained by the Moyal quantization procedure, is solved analytically. Its solutions exhibit two different confinement mechanisms — dependent on the sign of the coupling λ to the nonstandard gravitational fields. For λ >0 confinement is due to a rising potential, whereas for λ<0 it is due to the dynamical (geometric) bag formation. Numerical results for the corresponding energy spectra are given. For a particular relation between two coupling constants, the model fits into the scheme of supersymmetrical quantum mechanics.