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We show that the spectral theory of the Dirac operator $D = i\delsl-\sigma(x)-i\pi(x)\gam_5$ in a static background $(\sigma(x),\pi(x))$ in 1+1 space-timedimensions, is underlined by a certain generalization of supersymmetric quantummechanics, and explore its consequences.Comment: latex, 18 page

The Dirac operator in a fermion bag background in 1+1 dimensions and generalized supersymmetric quantum mechanics