Discussion Overview
The discussion revolves around finding the 3x3 matrix representation of SU(2), specifically focusing on rotation matrices for particles with spin 1. Participants are seeking explicit forms of the generators of SU(2) in this context.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant requests the 3x3 matrix representation of SU(2) for spin 1 particles.
- Another participant provides a link to a PDF that discusses the isomorphism between SU(2)/Z2 and SO(3).
- A participant expresses interest in the generators of SU(2) specifically for a spin 1 particle, asking for explicit forms of the 3x3 matrices.
- One participant mentions that the three-dimensional irreducible representation of SU(2) can be realized as the symmetric square of the standard representation, but seeks clarification on this point.
- Another participant acknowledges the need for commutation relations and requests a reference for the explicit form of the matrices used for rotations around the z-axis for a spin 1 particle.
- A participant seeks clarification on the meaning of the symmetric square of the standard representation and requests a reference for it.
Areas of Agreement / Disagreement
Participants do not seem to reach a consensus on the specific form of the 3x3 matrices or the references needed, indicating that multiple views and uncertainties remain in the discussion.
Contextual Notes
There are limitations regarding the explicit forms of the matrices and the references to the representations being discussed. The discussion also reflects a dependence on definitions and unresolved mathematical steps related to the generators of SU(2).