Pauli matrices

The Pauli matricesMathworldPlanetmath are a set of three Hermitian, unitary matricesMathworldPlanetmath used by Wolfgang Pauli in his theory of quantum-mechanical spin. They are given by:

σ1 =(0110)
σ2 =(0-ii0)
σ3 =(100-1)

They satisfy the following commutation and anticommutation identities:

[σi,σj] =2iϵijkσkwhere ϵijk is the Levi-Civita symbol
{σi,σj} =2𝐈δijwhere 𝐈 is the identity matrix and δij is the Kronecker delta

0.1 Delta notation

With the identity matrixMathworldPlanetmath I, the Pauli matrices form a group. When combined in this way, they are often given the symbols δi, as follows:

δ0 =(1001)
δ1 =(0110)
δ2 =(0-ii0)
δ3 =(100-1)

This choice is useful when writing the Dirac matrices.

Title Pauli matrices
Canonical name PauliMatrices
Date of creation 2013-03-22 17:57:01
Last modified on 2013-03-22 17:57:01
Owner invisiblerhino (19637)
Last modified by invisiblerhino (19637)
Numerical id 9
Author invisiblerhino (19637)
Entry type Definition
Classification msc 15A57
Synonym sigma matrices
Related topic Spinor
Related topic SchrodingersWaveEquation
Related topic UnitaryGroup
Related topic HermitianMatrix
Related topic DiracMatrices
Related topic DiracEquation