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
are
Pauli matrices
while
and
are the
unit and zero matrix respectively. Dirac matrices may be used to factorize the
Klein–Gordon equation:
where
is the
d'Alembert operator.
Introduced by
P. Dirac
in
1928
in the derivation of the Dirac equation.