Dirac sea
The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles with negative energy. It was first postulated by the British physicist Paul Dirac in 1930 to explain the anomalous negative-energy quantum states predicted by the Dirac equation for relativistic electrons. The positron, the antimatter counterpart of the electron, was originally conceived of as a hole in the Dirac sea, well before its experimental discovery in 1932.
Upon solving the free Dirac equation,
one finds
where
for plane wave solutions with 3-momentum p. This is a direct consequence of the relativistic energy-momentum relation
upon which the Dirac equation is built. The quantity U is a constant 2 × 1 column vector and N is a normalization constant. The quantity ε is called the time evolution factor, and its interpretation in similar roles in, for example, the plane wave solutions of the Schrödinger equation, is the energy of the wave (particle). This interpretation is not immediately available here since it may acquire negative values. A similar situation prevails for the Klein–Gordon equation. In that case, the absolute value of ε can be interpreted as the energy of the wave since in the canonical formalism, waves with negative ε actually have positive energy Ep. But this is not the case with the Dirac equation. The energy in the canonical formalism associated with negative ε is –Ep.
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