The group properties of dirac's operators

Abstract

The wave-equation for the spinning electron devised by Dirac has the form {α∂/∂ x + ᵝ∂/∂ y + γ∂/∂ z + δ∂/∂( ict ) + 2π imc / h } ψ = 0 in free space, the symbol ψ standing for an ordered set of four wave-functions (ψ 1 , ψ 2 , ψ 3 , ψ 4 ), operated on by the matrices α, β, γ, δ. These matrices satisfy the equations α 2 = 1, β 2 = 1, ... αβ + βα = 0, ... which will be referred to as “ Dirac’s equations.”