Dirac equation

In <a href="/facts/Particle_physics/YgIuyj2t">particle physics</a>, the Dirac equation is a <a href="/facts/Relativistic_wave_equation/UVF8oBjd">relativistic wave equation</a> derived by British physicist <a href="/facts/Paul_Dirac/6bt5yRdk">Paul Dirac</a> in 1928. In its free form, or including electromagnetic interactions, it describes all <a href="/facts/Spin-1/2/3I929M4X">spin-1/2</a> <a href="/facts/Massive_particle/h9KArL5q">massive particles</a>, called "Dirac particles", such as <a href="/facts/Electron/L0KBo5cW">electrons</a> and <a href="/facts/Quark/hwuuVkV5">quarks</a> for which <a href="/facts/Parity_(physics)/emSbJ4hD">parity</a> is a <a href="/facts/Symmetry_(physics)/gJmgsooI">symmetry</a>. It is consistent with both the principles of <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a> and the theory of <a href="/facts/Special_relativity/vsFFc63E">special relativity</a>, and was the first theory to account fully for special relativity in the context of quantum mechanics. It was validated by accounting for the <a href="/facts/Fine_structure/6lejlmN2">fine structure</a> of the <a href="/facts/Hydrogen_spectral_series/BhTeHzBt">hydrogen spectrum</a> in a completely rigorous way. It has become vital in the building of the <a href="/facts/Standard_Model/LhVGf9ow">Standard Model</a>.
The equation also implied the existence of a new form of matter, <a href="/facts/Antimatter/NvpGDLof">antimatter</a>, previously unsuspected and unobserved and which was experimentally confirmed several years later. It also provided a theoretical justification for the introduction of several component wave functions in <a href="/facts/Wolfgang_Pauli/Ugk4ubXk">Pauli</a>'s <a href="/facts/Phenomenology_(particle_physics)/390KC4vG">phenomenological</a> theory of <a href="/facts/Spin_(physics)/4Jvp7e8P">spin</a>. The wave functions in the Dirac theory are vectors of four <a href="/facts/Complex_number/2w7mqI7e">complex numbers</a> (known as <a href="/facts/Bispinor/wm8UNWxJ">bispinors</a>), two of which resemble <a href="/facts/Pauli_equation/gdPIf0cw">the Pauli wavefunction</a> in the non-relativistic limit, in contrast to the <a href="/facts/Schr%C3%B6dinger_equation/3csgSIWF">Schrödinger equation</a> which described wave functions of only one complex value. Moreover, in the limit of zero mass, the Dirac equation reduces to the <a href="/facts/Weyl_equation/8KhWTFaM">Weyl equation</a>.
In the context of <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theory</a>, the Dirac equation is reinterpreted to describe quantum fields corresponding to spin-1⁄2 particles.
Dirac did not fully appreciate the importance of his results; however, the entailed explanation of spin as a consequence of the union of quantum mechanics and relativity—and the eventual discovery of the <a href="/facts/Positron/HgV4zBzA">positron</a>—represents one of the great triumphs of <a href="/facts/Theoretical_physics/Cs2Y12rQ">theoretical physics</a>. This accomplishment has been described as fully on par with the works of <a href="/facts/Isaac_Newton/4L7gTncN">Newton</a>, <a href="/facts/James_Clerk_Maxwell/jtYyze61">Maxwell</a>, and <a href="/facts/Albert_Einstein/CNTet8qu">Einstein</a> before him. The equation has been deemed by some physicists to be the "real seed of modern physics". The equation has also been described as the "centerpiece of relativistic quantum mechanics", with it also stated that "the equation is perhaps the most important one in all of quantum mechanics".
The Dirac equation is inscribed upon a plaque on the floor of <a href="/facts/Westminster_Abbey/txMva2Xf">Westminster Abbey</a>. Unveiled on 13 November 1995, the plaque commemorates Dirac's life.

Dirac equation open-in-new

Dirac equation