ABSTRACT
In the Dirac equation we encountered an additional difficulty, namely that the negative energy solutions even arise at the level of the classical theory. In field theory the negative energy solutions had an interpretation in terms of antiparticles, and the field theory Hamiltonian was still positive. A hole in the Dirac sea is by definition the state that is obtained by annihilating a negative energy state in the Dirac sea. As annihilation lowers the total energy by the energy of the annihilated state, which in this case is negative, the net energy is raised. The vacuum value of the operator is indicated by the constant, which can be normalised to zero.
