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/ d e i \ (is) y — r*?W' = -/"Y'. \dx* c h / The factor — r on the right-hand side of this equation shows that the Dirac equation for an electron is not invariant under inversions. However, if we set 0? = O and JU = 0, then equation (15) is numerically invariant under inversions. This is done in the neutrino theory of light. Hence that theory has the same invariance properties as the Maxwell theory. Veblenf and DiracJ have both shown that there is no nonsingular analog of the Dirac equation which is conformally invariant. The result given here shows how the invariance fails. We have given the detailed treatment of the behavior of the Dirac equation under the four-dimensional inversion; the three-dimensional inversion may be treated by restricting the range of indices in (7), (8), and (12) to 1, 2, 3 and adding the equation x* = x to (7).

Note on degree of trigonometric and polynomial approximation to an analytic function