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arXiv · 1411.7867

Symmetries of the Schr\"odinger Equation and Algebra/Superalgebra Duality

Francesco Toppan
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Abstract

Some key features of the symmetries of the Schr\"odinger equation that are common to a much broader class of dynamical systems (some under construction) are illustrated. I discuss the algebra/superalgebra duality involving first and second-order differential operators. It provides different viewpoints for the spectrum-generating subalgebras. The representation-dependent notion of on-shell symmetry is introduced. The difference in associating the time-derivative symmetry operator with either a root or a Cartan generator of the $sl(2)$ subalgebra is discussed. In application to one-dimensional Lagrangian superconformal sigma-models it implies superconformal actions which are either supersymmetric or non-supersymmetric.

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Francesco Toppan. 2014-11-28. Symmetries of the Schr\"odinger Equation and Algebra/Superalgebra Duality. https://doi.org/10.1088/1742-6596/597/1/012071

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