The Dirac equation is an equation from quantum mechanics. Paul Dirac formulated the equation in 1928. The equation describes the behaviour of fermions (e.g. electrons), and takes special relativity into account. The equation showed the existence of antimatter.
- It does not change in Lorentz transformation. This means it is a differential equation of the same order in space and time.
- The Pauli equation can be derived from a special case of the equation
- It predicts the existence of antimatter particles, with the same mass and spin, but with the opposite charge. In 1931, Dirac predicted the existence of positrons, one year before the particles were found in an experiment.
- It explains why the spin of the electrons in the Stern–Gerlach experiment acts like a magnet, which splits the silver atoms according to their spin.
- The differential operator used in a special form of the equation is very important for differential geometry