Pauli Terms Must Be Absent In Dirac Equation

Details Pauli Terms Must Be Absent In Dirac Equation Pauli Terms Must Be Absent In Dirac Equation

2000-05-20

arxiv.org/abs/hep-th/0005191v1

Physics

High Energy Physics

High Energy Physics - Theory

10 pages

Scientific paper

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' $\sigma^{\mu\nu}$ 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 $Cl_D$ because the $\sigma^{\mu\nu}$ are excluded).

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