# SU(2) in 3-d

1. Mar 25, 2012

### 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!

2. Mar 26, 2012

### quasar987

3. Mar 27, 2012

### 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)

4. Mar 27, 2012

### Bill_K

(Si)jk = εijk

5. Mar 27, 2012

### 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.

6. Mar 27, 2012

### 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!

7. Mar 27, 2012

### 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?