Dirac equation

A relativistic quantum wave equation for spin-½ particles. Its structure accounts for electron spin and implies corresponding antiparticles, including the positron.

Dirac spinor: A multi-component wavefunction that describes a spin-½ particle in the Dirac equation. Its components encode the electron’s spin states and particle–antiparticle solutions.
Special relativity: A theory relating space and time for inertial observers, with invariant light speed and Lorentz transformations. The equation is built to respect relativistic energy and momentum.
Paul Dirac: An English theoretical physicist who developed the Dirac equation and made foundational contributions to quantum theory. He formulated the equation in 1928 to reconcile quantum mechanics with special relativity.
Quantum electrodynamics: The quantum field theory of electromagnetic interactions between charged particles and photons. Its electron field is described by the Dirac equation coupled to the electromagnetic field.
Weyl equation: A relativistic equation describing massless spin-½ fields of definite chirality. It is a massless chiral specialization related to the Dirac equation.
Dirac matrices: Matrices satisfying anticommutation relations that let the Dirac equation reproduce relativistic energy and momentum. They make the equation linear in both time and spatial derivatives.
Quantum mechanics: A physical theory describing matter and radiation through states, probabilities, and observables. The Dirac equation applies quantum wave dynamics to relativistic particles.
Schrödinger equation: The fundamental nonrelativistic equation governing the time evolution of quantum states. Its success for slow particles left the relativistic electron problem unresolved.
Dirac equation in an electromagnetic field: The Dirac equation with electromagnetic interactions introduced through a gauge potential. This form describes charged relativistic particles interacting with electric and magnetic fields.
Majorana equation: A relativistic wave equation for neutral spin-½ fields that can be their own antiparticles. It contrasts with the usual Dirac description, in which particle and antiparticle are distinct.

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