The Dirac equation describes the relativistic behavior of spin-½ particles such as electrons.
Paul Dirac published the equation in 1928 to combine quantum mechanics with special relativity. Unlike the nonrelativistic Schrödinger equation, it treats time and space in a relativistically compatible way and naturally incorporates the electron’s intrinsic spin.
The equation initially produced solutions with negative energy. Dirac’s interpretation of these solutions helped inspire the prediction of antimatter, and the positron was discovered experimentally by Carl Anderson in 1932. Quantum field theory later gave the modern interpretation: particles and antiparticles are excitations of corresponding fields.
The Dirac equation also predicts the electron’s magnetic moment to a close approximation. Its limitations appear when particle creation and annihilation become important, where quantum electrodynamics provides the more complete framework. The equation remains fundamental in particle physics and is also used in condensed-matter models of Dirac materials.