Abstract
We obtain a scalar field theory by applying a specific Higgs mechanism on SYM and imposing a constraint. We see that the resulting relativistic equation describes a charged particle non-minimally coupled to the Coulomb potential. The resulting non-minimal coupling allows us to build a relativistic Runge-Lenz vector that generates, together with the angular momentum, the SO(4) algebra. We also construct a Kustaanheimo-Stiefel duality between this modified relativistic Coulomb problem and the modified relativistic harmonic oscillator and see how the integrals of motion of both problems are mapped.
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