Finding the 3x3 Matrix Representation of SU(2)

[QuantumLeak]

Hi all,
do you know where i can find the 3x3 matrix representation of SU(2)? Which means basically rotation matrices for particles of spin 1.

Thanks!

 

[quasar987]

Google yielded the following pdf: http://www.mat.univie.ac.at/~westra/so3su2.pdf

 

[QuantumLeak]

That pdf shows the isomorphism between SU(2)/Z2 and SO(3). What I would like to find is the generators of SU(2) for a S=1 spin particle, i.e. 3x3 generators of SU(2)

 

[Bill_K]

(S_i)_jk = ε_ijk

 

[martinbn]

The three dimensional irreducible representation of SU(2) can be realized as the symmetric square of the standard representation. But I am not sure what exactly you are looking for. May be you are asking about the representation of the Lie algebra and the matrices by which the standard basis elements act.

 

[QuantumLeak]

Yes Bill I know the commutation relation that they have to satisfy. What I need is a reference with the explicit form of 3x3 matrices of the generators. In other words, if I have to make a rotation of an angle \alpha around the z axis of a spin 1 particle, which matrix I have to use to model this rotation?

martin what do you mean by symmetric square of standard representation? Do you have a reference?

Thanks!

 

[QuantumLeak]

Oh, sorry Bill now I see. you mean that the jk element of the matrix of the i-th commutator has to satisfy that relation. Ok thanks. Do you have a textbook reference for that?