The Dirac equation without spinors

TL;DR

This paper presents a tensor formulation of the Dirac equation and analyzes a simplified model that mimics its properties in weak external fields, offering a new perspective on spinor-free representations.

Contribution

It introduces a tensor-based version of the Dirac equation and studies a simplified model with similar properties, avoiding spinors.

Findings

Tensor formulation of Dirac equation provided

Model exhibits Dirac-like properties in weak fields

Potential simplification for understanding Dirac dynamics

Abstract

In the first part of the paper we give a tensor version of the Dirac equation. In the second part we formulate and analyse a simple model equation which for weak external fields appears to have properties similar to those of the 2--dimensional Dirac equation.