ABSTRACT
This chapter discusses the form of both the positiveand negative-energy solutions of the Dirac equation, and we shall then concentrate on the physical interpretation of the negative-energy solutions of both the Dirac and the KG equations. The degree of freedom is, of course, spin – an entirely quantum mechanical angular momentum, analogous to orbital angular momentum. Four-momentum is the only physical property of a particle obeying the Dirac equation. In order to prevent positive-energy electrons making transitions to the lower, negative-energy states, Dirac postulated that the normal ‘empty’, or ‘vacuum’, state – that with no positive-energy electrons present – is such that all the negative-energy states are filled with electrons. The Pauli exclusion principle then forbids any positive-energy electrons from falling into these lower energy levels.
