Chapter 1 Relativistic Theory and Electron Spin

The efforts to formulate a relativistic quantum mechanics began with at-tempts to apply the correspondence principle to attain a relativistic wave equation replacing the Schrödinger equation. The first equation was pro-posed by E. Schrödinger(in 1926), W. Gordon(in 1926), and O. Klein(in 1927), which was initially not well recognized due to its negative probabil-ity densities. Another equation was proposed by P. A. M. Dirac in 1928. The former equation is a scalar wave equation of second order while the latter one is a spinor wave equation of first order. We will mainly focus on the Dirac equation and its implications together with some of recent developments. It is conceptually easier for undergraduates to investigate the features of the Dirac equation in its interpretation as a single-particle wave equation. For the purpose of a heuristic mode of teaching, we will start this chapter by following the historical development rather than the axiomatic procedure of quantum field theory.