Dyon-Oscillator Duality

TL;DR

This paper explores a duality in quantum mechanics where oscillator-like systems are mathematically equivalent to atomic systems involving dyons, providing insights into nonrelativistic dualities similar to Seiberg-Witten theory.

Contribution

It introduces the concept of dyon-oscillator duality as a prototype for nonrelativistic Seiberg-Witten duality, linking oscillator systems to charged particle-dyon atomic systems.

Findings

Establishes a duality between oscillator-like systems and dyonic atomic systems.

Provides a theoretical framework connecting nonrelativistic quantum mechanics and duality concepts.

Highlights the role of magnetic and electric charges in quantum dualities.

Abstract

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.