Symmetry, Integrability and Geometry: Methods and Applications | 2021
Z23-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics
Abstract
Quantum mechanical systems whose symmetry is given by Z2-graded version of superconformal algebra are introduced. This is done by finding a realization of a Z2-graded Lie superalgebra in terms of a standard Lie superalgebra and the Clifford algebra. The realization allows us to map many models of superconformal quantum mechanics (SCQM) to their Z2-graded extensions. It is observed that for the simplest SCQM with osp(1|2) symmetry there exist two inequivalent Z2-graded extensions. Applying the standard prescription of conformal quantum mechanics, spectrum of the SCQMs with the Z2-graded osp(1|2) symmetry is analyzed. It is shown that many models of SCQM can be extended to Z2 -graded setting.