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.
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