Four Hermitian matrices , , and of dimension which satisfy the following conditions
where is the unit matrix of dimension . The matrices may also be replaced by the Hermitian matrices , and by the anti-Hermitian matrix , which satisfy the condition
where , ; if , , which makes it possible to write the Dirac equation in a form which is covariant with respect to the Lorentz group of transformations. The matrices , and are defined up to an arbitrary unitary transformation, and may be represented in various ways. One such representation is
where is the d'Alembert operator.
Introduced by P. Dirac in 1928 in the derivation of the Dirac equation.
For references see – of Dirac equation.
Dirac matrices. V.D. Kukin (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Dirac_matrices&oldid=11569