Mathematical Structure
The defining property for the gamma matrices to generate a Clifford algebra is the anticommutation relation
where is the anticommutator, is the Minkowski metric with signature (+ − − −) and is the 4x4 unit matrix.
This defining property is considered to be more fundamental than the numerical values used in the gamma matrices. Covariant gamma matrices are defined by
and Einstein notation is assumed.
Note that the other sign convention for the metric, (− + + +) necessitates either a change in the defining equation:
or a multiplication of all gamma matrices by, which of course changes their hermiticity properties detailed below. Under the alternative sign convention for the metric the covariant gamma matrices are then defined by
- .
Read more about this topic: Gamma Matrices
Famous quotes containing the words mathematical and/or structure:
“The circumstances of human society are too complicated to be submitted to the rigour of mathematical calculation.”
—Marquis De Custine (1790–1857)
“The structure was designed by an old sea captain who believed that the world would end in a flood. He built a home in the traditional shape of the Ark, inverted, with the roof forming the hull of the proposed vessel. The builder expected that the deluge would cause the house to topple and then reverse itself, floating away on its roof until it should land on some new Ararat.”
—For the State of New Jersey, U.S. public relief program (1935-1943)