The square root of the Dirac operator on the superspace and the Maxwell equations

TL;DR

This paper explores the process of deriving Maxwell equations and the Dirac equation from the square root of the Dirac operator within superspace, connecting superfield formalism to fundamental equations of physics.

Contribution

It demonstrates that taking the square root of the Dirac operator on superspace naturally yields superfield W_ and the correct equations of motion, including Maxwell and massless Dirac equations.

Findings

Derivation of Maxwell equations from superspace formalism

Connection between superfield W_ and equations of motion

Validation of the square root procedure for Dirac operator

Abstract

We re-consider the procedure of ``taking a square root of the Dirac equation'' on the superspace and show that it leads to the well known superfield W_\alpha and to the proper equations of motion for the components, i.e. the Maxwell equations and the massless Dirac equation.