A New Supersymmetric Extension of Conformal Mechanics

TL;DR

This paper introduces a novel supersymmetric extension of conformal mechanics with geometrically meaningful variables, analyzing its superalgebra and providing a superfield-based method for exact solutions.

Contribution

It presents a new supersymmetric extension of conformal mechanics with geometrical interpretation and detailed superalgebra analysis, including a superfield approach for solutions.

Findings

Super-Hamiltonian as Lie-derivative of conformal mechanics

Extended conformal generators with 'square-root' relations

Superfield constraint yields exact solutions

Abstract

In this paper a new supersymmetric extension of conformal mechanics is put forward. The beauty of this extension is that all variables have a clear geometrical meaning and the super-Hamiltonian turns out to be the Lie-derivative of the Hamiltonian flow of standard conformal mechanics. In this paper we also provide a supersymmetric extension of the other conformal generators of the theory and find their "square-roots". The whole superalgebra of these charges is then analyzed in details. We conclude the paper by showing that, using superfields, a constraint can be built which provides the exact solution of the system.