  The Dirac negative energy sea introduced the concept of antimatter, and
explained it, not least in its relationship to negative-energy solutions to the
wave equation. Post-war, it was largely displaced by what I shall call the
'standard formalism', dependent, among other things, on normal-ordering. A much
better explanation is provided by the 'two complex structures' viewpoint, as
first introduced by Irving Segal: the one ('natural') kind of complex numbers
at the level of covariant, local fields; and the other ('particle') complex
numbers at the level of the one-particle Hilbert space and Fock space. The
former is local, the latter non-local: therein lies the fundamental difference
between relativistic and non-relativistic quantum theory.
