# Towards differential elimination of spinor field from spinor electrodynamics

## TL;DR

This paper investigates the possibility of eliminating a spinor component from spinor electrodynamics equations, proposing a Lagrangian formulation that retains the same physics with fewer variables.

## Contribution

It introduces a Lagrangian depending on the electromagnetic field and one spinor component, offering a new approach to simplify spinor electrodynamics equations.

## Key findings

- A PDE system with one spinor component is equivalent to full spinor electrodynamics.
- A Lagrangian formulation with reduced variables can describe the same physics.
- Potential simplification of spinor electrodynamics equations through differential elimination.

## Abstract

A system of PDEs for the electromagnetic field and one real component of the spinor field is generally equivalent to spinor electrodynamics. There are reasons to believe that the component can be differentially eliminated from the system. A Lagrangian depending on the electromagnetic field and one real component of the spinor field generally describes the same physics as spinor electrodynamics.