Supersymmetric Extension of the Snyder Algebra

TL;DR

This paper introduces a minimal supersymmetric extension of the Snyder algebra, resulting in a discrete space lattice compatible with supersymmetry, and explores its representations.

Contribution

It presents a novel minimal supersymmetric extension of the Snyder algebra that does not rely on super-de Sitter groups, differing from previous approaches.

Findings

Position spectra are discrete, indicating a lattice structure of space.

The supersymmetric lattice is consistent with supersymmetry transformations.

The construction provides a new framework for supersymmetric quantum space models.

Abstract

We obtain a minimal supersymmetric extension of the Snyder algebra and study its representations. The construction differs from the general approach given in Hatsuda and Siegel ({\tt hep-th/0311002}), and does not utilize super-de Sitter groups. The spectra of the position operators are discrete, implying a lattice description of space, and the lattice is compatible with supersymmetry transformations.