SU(2) in 3-d

  • #1
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!
 

Answers and Replies

  • #3
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)
 
  • #5
martinbn
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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
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
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?
 

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