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 $C{l}_D.$ These include the 6 `tensorial' ${\sigma }^{\mu \nu }$ with which the `Pauli terms' are formed. We find that these violate a basic axiom of any *-algebra, when Dirac's $\Psi$ is canonical. Then the Dirac operator is spanned only by the 10 elements $1,i{\gamma }_5,{\gamma }^{\mu },{\gamma }^{\mu }{\gamma }_5$ (which don't form a basis of $C{l}_D$ because the ${\sigma }^{\mu \nu }$ are excluded).

10 pages