**Explanation from the Kaehler Calculus of Why Positrons Spuriously Emerge
with Negative Energy in Dirac's Theory**

**Abstract:**

This poster is the second complement to the talk by the present author "A
unifying calculus for physics: a demonstration in relativistic quantum
mechanics".

Though the mother equation obtained in the first poster has large (or even)
and small (odd) components, both of them belong to the electron, if one has
picked its ideal. We now choose the positron's ideal and obtain a very
similar mother system and the same Hamiltonian, except that the large
components are now odd and the small components are now even.

We return to the mother system for the electron, which we transform in such
a way that the role of the large and small components is reversed. This is
achieved by time and (sign of) charge reversal, but the role of the
potential energy term is now played by the potential energy minus twice the
rest mass. This amounts to having the total energy decreased by 2*mc*^{2}, or as
if the rest energy were the negative of the usual one. This is a consequence
of incorrectly treating the small components as if they constituted the wave
function of the antiparticle.