Dirac Matrices in Higher Dimensions


	It is possible to define Dirac matrices for dimensions higher than four using Kronecker products of Pauli matrices. For dimension , there are Dirac matrices, and the dimension of the matrices is .


	Contributed by: Enrique Zeleny
	Show Initialization Code

A. Pais, "On Spinors in n Dimensions," Journal of Mathematical Physics, 3(6), 1962.

Starting with Pauli matrices

, with

, define

where

For odd dimensions, the additional generator (a generalization of

) is

The Dirac matrices satisfy canonical anti-commutation relation

The above definition corresponds to the so-called "chiral basis," where Dirac matrices are block anti-diagonal. Other bases are possible, and are related to the chiral basis by rotations.

The Dirac matrices generate Euclidean Clifford algebra.