Four dimensional cubic supersymmetry

TL;DR

This paper explores a novel four-dimensional algebra extending the Poincaré algebra, distinct from supersymmetry, including its representations, invariant Lagrangian, and implications for Noether's theorem.

Contribution

It introduces a new four-dimensional algebra extending Poincaré, with detailed representation theory and an explicit invariant Lagrangian, differing from traditional supersymmetry.

Findings

Developed a non-trivial algebra extension of Poincaré in four dimensions.

Constructed the algebra's representations and invariant Lagrangian.

Discussed the implications for Noether's theorem.

Abstract

A four dimensional non-trivial extension of the Poincar\'e algebra different from supersymmetry is explicitly studied. Representation theory is investigated and an invariant Lagrangian is exhibited. Some discussion on the Noether theorem is also given.