Possible confinement mechanisms for nonrelativistic particles on a line

Details Possible confinement mechanisms for nonrelativistic particles on a line Possible confinement mechanisms for nonrelativistic particles on a line

2001-04-30

arxiv.org/abs/hep-th/0104261v1

Mod.Phys.Lett. A16 (2001) 1919

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1142/S0217732301005278

The gauge model of nonrelativistic particles on a line interacting with nonstandard gravitational fields [5] 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 Schr\"{o}dinger equation, obtained by the Moyal quantization procedure, is solved analytically. Its solutions exhibit two different confinement mechanisms - dependent on the sign of the coupling $\lambda$ to the nonstandard gravitational fields. For $\lambda>0$ confinement is due to a rising potential whereas for $\lambda<0$ it is due to 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.

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