Is supersymmetry around us?

Anzor Khelashvili (HEPI, Tbilisi State University / SANGU, Tbilisi)

Abstract: The Dirac Hamiltonian in arbitrary central potential admits presence of N=2 Witten's superalgebra. Invariance under this superalgebra gives the conserved generators only for the Coulomb-like potentials. It is so, both when a potential is a fourth component of the Lorentz-vector as well as a pure Lorentz-scalar. In the non-relativistic limit, these generators are related to the well-known Laplace-Runge-Lentz vector. Hydrogen atom spectra is derived algebraically in both cases. It is shown that this symmetry forbids the Lamb shift.