Derivation of the Dirac Equation from the Wave Equation of the Vacuum

In this chapter, we show that the Dirac equationDirac equation can be derived naturally based on the quantum wave modelQuantum wave model. In fact, the Dirac equationDirac equation is a direct consequence of the wave equation of the vacuumWave equation of the vacuum. Since the electronElectron is a massive particleParticle, according to our model, the Dirac equationDirac equation should be a special case of the Klein–Gordon equationKlein-Gordon equation. Its waveWave function represents only the longitudinal component of matter waveMatter wave. In the case of an electronElectron, its waveWave function can be represented by a 4-component column matrix. Then, it is easy to see that the Dirac equationDirac equation is a linearized waveWave equation which can be obtained directly by factorizing the Klein–Gordon equationKlein-Gordon equation.