Wolfram Research

Mathematica MathWorld Wolfram Science More »

HOME

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.

Dirac Matrices (Wolfram MathWorld)

Pauli Matrices (Wolfram MathWorld)

Matrix Direct Product (Wolfram MathWorld)

Spinor (Wolfram MathWorld)

Clifford Algebra (Wolfram MathWorld)

"Dirac Matrices in Higher Dimensions" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/DiracMatricesInHigherDimensions/

Contributed by: Enrique Zeleny

Report an issue »

Interact with Demonstrations using the latest version of the free Mathematica Player—Download Now

Browse all topics

	Source page:
	Email	Name (optional)
	Occupation (optional)	Organization (optional)
	I use Mathematica often occasionally never
	Country (optional) Remember me
	Note: Please do not include anything you consider confidential or proprietary. Your message and contact information may be shared with the author of any specific Demonstration for which you give feedback, but will not otherwise be published or distributed. Privacy Policy »

Wolfram Research

Site Index

RSS

Atom