The Dirac Equation

This lecture discusses the historical context leading to the development of the Dirac equation in 1928, which addressed the issues of negative energy solutions and negative particle densities in the Klein-Gordon equation. The Dirac equation, being first-order throughout, fully described the intrinsic spin and magnetic moment of the electron. It introduces Dirac spinors, four-component wave functions, and Dirac gamma matrices. The solutions of the Dirac equation for particles at rest are explored, revealing positive and negative energy solutions. Dirac's explanation for negative energy solutions, the concept of the Dirac sea, and the discovery of the anti-electron by Anderson in 1932 are also covered. The lecture concludes with the Feynman-Stückelberg Interpretation, proposing the existence of antiparticles for each known particle.