arXiv subjects
Publications and source records attributed to V. Ter-Antonyan.
The dyon-oscillator duality presented in this lecture can be treated as a prototype of the Seiberg-Witten duality in nonrelativistic quantum mechanics. The key statement declares that in some spatial dimensions the oscillator-like systems are dual to the atoms composed of the electrical charged particle and dyon, i.e., monopoles provided by both magnetic and electric charge.
It is shown that in one spatial dimension the quantum oscillator is dual to the charged particle situated in the field described by the superposition of Coulomb and Calogero-Sutherland potentials.
We have discussed the energy levels and probability distribution density for a quantum particle placed in the two-dimensional sombrero-shaped potential $V(ρ,ρ_0)=μω^2|ρ^2-ρ_0^2|/2$.
It is shown, that the reduction of the circular quantum oscillator by the $Z_2$-group action results to the two systems: a two-dimensional hydrogen atom, and a ``charge - charged magnetic vortex" one, with the spin $\frac 12$. Analogously, the $Z_N$-reduction of the two-dimensional system with the central potential $r^{2(N-1)}$ results into $N$ bound ``charge - magnetic vertex" systems with the interaction potential $r^{2(1/N-1)}$ and spins $σ=\frac kN$, $k =0,1,..., (N-1)$.