Supersymmetric Oscillator: Novel Symmetries

TL;DR

This paper explores the symmetries of the supersymmetric harmonic oscillator, revealing new discrete symmetries and connecting them to differential geometry, with implications for theoretical physics.

Contribution

It introduces a novel set of discrete symmetries in the supersymmetric oscillator, expanding understanding of its mathematical and physical properties.

Findings

Discovery of new discrete symmetries in SHO

Connection between symmetries and differential geometry

Discussion of physical relevance of symmetries

Abstract

We discuss various continuous and discrete symmetries of the supersymmetric simple harmonic oscillator (SHO) in one (0 + 1)-dimension of spacetime and show their relevance in the context of mathematics of differential geometry. We show the existence of a novel set of discrete symmetries in the theory which has, hitherto, not been discussed in the literature on theoretical aspects of SHO. We also point out the physical relevance of our present investigation.