Dirac equation

In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin- ⁠1/2⁠ massive particles, called "Dirac particles", such as electrons and quarks for which parity is a symmetry. It is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to fully account for special relativity in the context of quantum mechanics. The equation is validated by its rigorous accounting of the observed fine structure of the hydrogen spectrum and has become vital in the building of the Standard Model.

The equation also implied the existence of a new form of matter, antimatter, previously unsuspected and unobserved. The existence of antimatter was experimentally confirmed several years later. It also provided a theoretical justification for the introduction of several component wave functions in Pauli's phenomenological theory of spin. The wave functions in the Dirac theory are vectors of four complex numbers (known as Dirac spinors), two of which resemble the Pauli wavefunction in the non-relativistic limit, in contrast to the Schrödinger equation, which described wave functions of only one complex value. Moreover, in the limit of zero mass, the Dirac equation reduces to the Weyl equation. In the context of quantum field theory, the Dirac equation is reinterpreted to describe quantum fields corresponding to spin-⁠1/2⁠ particles.