Symmetries of the Schr?dinger equation and algebra/superalgebra duality

30th International Colloquium on Group Theoretical Methods in Physics

Toppan, Francesco^1

CBPF, Rua Dr. Xavier Sigaud 150, Rio de Janeiro (RJ)

cep 22290-180, Brazil^1

关键词: Differential operators;    Key feature;    Lagrangian;    Second orders;    Sigma model;    Subalgebras;    Time derivative;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012071/pdf
DOI  :  10.1088/1742-6596/597/1/012071

来源: IOP

【 摘 要 】

Some key features of the symmetries of the Schrodinger 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.