(Super)symmetries of semiclassical models in theoretical and condensed matter physics

TL;DR

This paper explores symmetries in semiclassical models across physics, introducing a covariant algorithm for conserved quantities, and extending the formalism to supersymmetry and non-commutative systems, with applications in monopoles and curved space.

Contribution

It presents a covariant algorithm for deriving conserved quantities and extends the formalism to supersymmetry and non-commutative models in semiclassical physics.

Findings

Derived conserved quantities using van Holten's algorithm.

Extended formalism to supersymmetric systems.

Applied the framework to non-Abelian monopoles and curved spaces.

Abstract

Van Holten's covariant algorithm for deriving conserved quantities is presented, with particular attention paid to Runge-Lenz-type vectors. The classical dynamics of isospin-carrying particles is reviewed. Physical applications including non-Abelian monopole-type systems in diatoms, introduced by Moody, Shapere and Wilczek, are considered. Applied to curved space, the formalism of van Holten allows us to describe the dynamical symmetries of generalized Kaluza-Klein monopoles. The framework is extended to supersymmetry and applied to the SUSY of the monopoles. Yet another application concerns the three-dimensional non-commutative oscillator.