Novel symmetries in image supersymmetric quantum mechanical models Original Research Article

We demonstrate the existence of a novel set of discrete symmetries in the context of the image supersymmetric (SUSY) quantum mechanical model with a potential function image that is a generalization of the potential of the 1D SUSY harmonic oscillator. We perform the same exercise for the motion of a charged particle in the image–image plane under the influence of a magnetic field in the image-direction. We derive the underlying algebra of the existing continuous symmetry transformations (and corresponding conserved charges) and establish its relevance to the algebraic structures of the de Rham cohomological operators of differential geometry. We show that the discrete symmetry transformations of our present general theories correspond to the Hodge duality operation. Ultimately, we conjecture that any arbitrary image SUSY quantum mechanical system can be shown to be a tractable model for the Hodge theory.