Pauli Terms Must Be Absent In Dirac Equation

Abstract

It should be of interest, whether Dirac's equation involves all 16 basis elements of his Clifford algebra $Cl_D.$ These include the 6 `tensorial' $σ^{μν}$ with which the `Pauli terms' are formed. We find that these violate a basic axiom of any *-algebra, when Dirac's $Ψ$ is canonical. Then the Dirac operator is spanned only by the 10 elements $1,iγ_5,γ^μ,γ^μγ_5$ (which don't form a basis of $Cl_D$ because the $σ^{μν}$ are excluded).