The ##{\bf su}(2)## Lie algebra in a representation ##\bf R## is defined by(adsbygoogle = window.adsbygoogle || []).push({});

##[T^{a}_{\bf R},T^{b}_{\bf R}]=i\epsilon^{abc}T^{c}_{\bf R},##

where ##T^{a}_{\bf R}## are the ##3## generators of the algebra.

In ##2## dimensions, these generators are the Pauli matrices

##T^{1}_{\bf 1} = \frac{1}{2}\begin{pmatrix}0 & 1\\ 1 & 0 \end{pmatrix}, \qquad T^{2}_{\bf 1} = \frac{1}{2}\begin{pmatrix}0 & -i\\ i & 0 \end{pmatrix}, \qquad

T^{3}_{\bf 1} = \frac{1}{2}\begin{pmatrix}1 & 0\\ 0 & -1 \end{pmatrix}.##

In ##3## dimensions, these generators are

##T^{1}_{\bf 2} = \frac{1}{\sqrt{2}}\begin{pmatrix}0 & 1 & 0\\ 1 & 0 & 1\\ 0 & 1 & 0 \end{pmatrix}, \qquad T^{2}_{\bf 2} = \frac{1}{\sqrt{2}}\begin{pmatrix}0 & -i & 0\\ i & 0 & -i\\ 0 & i & 0 \end{pmatrix}, \qquad

T^{3}_{\bf 2} = \begin{pmatrix}1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{pmatrix}.##

------------------------------------------------------------------------------

1. How can you derive the generators in ##2## and ##3## dimensions?

2. What are the generators in ##1## dimension?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I ##SU(2)## generators in ##1##, ##2## and ##3## dimensions

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - ##SU generators ##1## | Date |
---|---|

I Can we construct a Lie algebra from the squares of SU(1,1) | Feb 24, 2018 |

I SU(2) generators | Jul 28, 2017 |

A Star groups SU*(N) | Feb 1, 2017 |

I SU(2) matrices | Nov 17, 2016 |

Generators of the SU(8) group | Jul 15, 2008 |

**Physics Forums - The Fusion of Science and Community**