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We study the supersymmetric quantum mechanics of an isospin particle in thebackground of spherically symmetric Yang-Mills gauge field. We show that on$S^{2}$ the number of supersymmetries can be made arbitrarily large for aspecific choice of the spherically symmetric SU(2) gauge field. However, thesymmetry algebra containing the supercharges becomes nonlinear if the number offermions is greater than two. We present the exact energy spectra andeigenfunctions, which can be written as the product of monopole harmonics and acertain isospin state. We also find that the supersymmetry is spontaneouslybroken if the number of supersymmetries is even.Comment: 6 page

ISOSPIN PARTICLE ON S2 WITH ARBITRARY NUMBER OF SUPERSYMMETRIES

ISOSPIN PARTICLE ON S² WITH ARBITRARY NUMBER OF SUPERSYMMETRIES