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Dirac matrices

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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.


Comments

For references see – of Dirac equation.

How to Cite This Entry:
Dirac matrices. V.D. Kukin (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Dirac_matrices&oldid=11569
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098