Discrete symmetries and supersymmetries of quantum-mechanical systems (Q2737719)

Conclusions: A new symmetry algebra for the Dirac equation (or the Schrödinger-Pauli equation) describing various quantum-mechanical systems has been derived. This algebra is based on discrete involutive symmetries of the considered systems and is of the biggest dimension from all known invariant algebras of the considered systems. NEWLINENEWLINENEWLINEThe new symmetry algebra was used for two purposes: i) to reduce the considered quantum-mechanical system to simpler subsystems and ii) to search for its supersymmetries (extended, reducible or generalized) and to explain degeneracy of its energy spectrum. NEWLINENEWLINENEWLINESince the required transformation properties of electromagnetic fields \(A_\mu(x)\) for the considered quantum-mechanical systems to be supersymmetric seem to be physically realisable (for details see [\textit{J. Niederle} and \textit{A. G. Nikitin}, J. Math. Phys. 40, No. 3, 1980-1993 (1999; Zbl 0960.81029)]), these systems give strong indications that supersymmetry is indeed a symmetry of nature.NEWLINENEWLINEFor the entire collection see [Zbl 0967.00038].