Supersymmetry without Grassmann Variables

TL;DR

This paper explores a formulation of supersymmetry that avoids Grassmann variables by using unitary operators, raising questions about its physical relevance and experimental testability.

Contribution

It introduces a Grassmann-free representation of supersymmetry using unitary operators, offering a potentially more physically relevant framework.

Findings

Supersymmetry can be represented without Grassmann variables.

The physical relevance depends on the ability to add states of different fermion numbers.

Experimental verification may soon be possible.

Abstract

Supersymmetry transformations may be represented by unitary operators in a formulation of supersymmetry without numbers that anti-commute. The physical relevance of this formulation hinges on whether or not one may add states of even and odd fermion number, a question which soon may be settled by experiment.