Two components relativistic quantum wave equation for scalar bosons

TL;DR

This paper introduces a new first-order relativistic quantum wave equation for scalar bosons with two components, analogous to the Dirac equation for fermions, and consistent with the Schrödinger equation in the non-relativistic limit.

Contribution

It proposes a novel two-component wave equation for scalar bosons that parallels the Dirac equation, differing from the Klein-Gordon equation.

Findings

The new equation is first order in time.

It reduces to Schrödinger equation non-relativistically.

Wave function has two components, similar to fermions.

Abstract

We show that, in the relativistic regime, scalar bosons satisfy a quantum wave equation which is quite analogous to the Dirac equation. In contrast with the Klein-Gordon equation it is first order with respect to time derivation. It leads in a regular way to the standard Schr\"odinger equation in the non-relativistic limit. There are two components for the wave function in this representation for the scalar boson, in a way completely analogous to the four components for the spin $1/2$ fermion in the Dirac equation.