Stability of the vacuum and quantization of the electron--positron field for the strong external fields

A method is given for quantizing the electron-positron field in the external field of a superheavy nucleus. In essence we redefine the vacuum to be the state in which all negative-energy solutions of the Dirac equation, including bound states, are occupied. Among other desirable features, this provides a natural description of the instability of the state conventionally labeled as the vacuum and a continuity in the physical description of the system as a function of the nuclear charge.