# Dirac Equation

In particle physics, the Dirac equation is a relativistic wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to fully account for relativity in the context of quantum mechanics. It accounted for the fine details of the hydrogen spectrum in a completely rigorous way. The equation also implied the existence of a new form of matter, antimatter, hitherto unsuspected and unobserved, and actually predated its experimental discovery. It also provided a theoretical justification for the introduction of several-component wave functions in Pauli's phenomenological theory of spin. Although Dirac did not at first fully appreciate what his own equation was telling him, his resolute faith in the logic of mathematics as a means to physical reasoning, his explanation of spin as a consequence of the union of quantum mechanics and relativity, and the eventual discovery of the positron, represents one of the great triumphs of theoretical physics, fully on a par with the work of Newton, Maxwell, and Einstein before him.

### Other articles related to "dirac equation, dirac, equation, equations":

Spin Connection - Applications
... The spin connection arises in the Dirac equation when expressed in the language of curved spacetime ... The Dirac matrices are contracted onto vierbiens, We wish to construct a generally covariant Dirac equation ... the spinor transforms as and is a genuine tensor and Dirac's equation is rewritten as ...
Fermionic Field - Dirac Fields
... example of a spin-1/2 fermion field is the Dirac field (named after Paul Dirac), and denoted by ψ(x) ... The equation of motion for a free field is the Dirac equation, where γμ are gamma matrices and m is the mass ... The simplest possible solutions to this equation are plane wave solutions, and ...
Dirac Equation In The Algebra Of Physical Space
... The Dirac equation, as the relativistic equation that describes spin 1/2 particles in quantum mechanics can be written in terms of the Algebra of physical space (APS), which is a case of a Clifford ... The Dirac equation in APS, including the electromagnetic interaction, reads Another form of the Dirac equation in terms of the Space time algebra was ... In general, the Dirac equation in the formalism of geometric algebra has the advantage of providing a direct geometric interpretation ...
Dirac Equation in Curved Spacetime
... The Dirac equation in curved spacetime can be written by using vierbein fields and the gravitational spin connection ... The vierbein defines a local rest frame, allowing the constant Dirac matrices to act at each spacetime point ... In this way, Dirac's equation takes the following form in curved spacetime Here eaμ is the vierbein and Dμ is the covariant derivative for fermion fields, defined as follows where σab is the ...
Foldy–Wouthuysen Transformation - Other Applications
... transform originally developed for the Dirac Equation has found applications in many situations such as Acoustics, and Optics ... areas such as atomic systems synchrotron radiation and derivation of the Bloch equation for polarized beams ... too one has a similar problem of understanding the relativistic wave equations as the nonrelativistic approximation plus the relativistic correction terms in ...

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