Interplay between Dynamic Systems Described by the Klein-Gordon and Dirac Equations

TL;DR

This paper demonstrates how, in two-dimensional spacetime, a free Klein-Gordon system can be transformed into a Dirac system through appropriate redefinitions of current and energy-momentum tensor.

Contribution

It reveals a novel connection between Klein-Gordon and Dirac equations in 2D spacetime via redefinition of key physical quantities.

Findings

Klein-Gordon system can be converted into Dirac system in 2D

Proper redefinition of current and energy-momentum tensor is essential

Establishes a new link between scalar and spinor field equations

Abstract

It is shown that in the two-dimensional space-time the dynamic system, described by the free Klein-Gordon equation, turns to the dynamic system, described by the free Dirac equation, provided the current and the energy-momentum tensor are redefined in a proper way.