Dirac studied the electron in complex spacetime. In 1928, Dirac published the Dirac equation. With the Dirac formalism, electron description is a mathematical object having four components and made the prediction of "negative energies". Dirac’s mechanics produce negative energy states (i.e., the Dirac sea). The Dirac formalism refocuses the concern from one single particle to a "sea" consisting of infinitely many particles. Dirac supposed that all the negative energy states are filled already.
Dirac then realized that there existed positively charged spin particle with exactly the same mass as the electron. Dirac proposed that every particle must have an antiparticle with an opposite charge. Antiparticles fill the Dirac sea (though they are not usually observed). Initially, Dirac tied this particle to the proton. After others (including Hermann Weyl, Robert Oppenheimer, and Igor Tamm) disproved this possibility, Dirac predicted a new particle, the positron. If negative energy is transformed into a positive energy state, the energy is perceived as a positron. Positron is the antiparticle of electron. Positrons are produced through pair production (bipolar coupling).
In relativistic quantum mechanics, Dirac's equation admits both positive and negative energy states. So, what is there to prevent a fermion from constantly radiating away energy, resulting in lesser and lesser energy, resulting in a huge instability? Dirac proposed almost all the negative energy states are filled by a sea of negative energy fermions. In modern treatments of quantum field theory, the Dirac sea is subtly introduced by having different definitions for the occupation number for positive and negative frequency decompositions.
The model of a negative energy "sea" of electrons has critics.
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