Talk:Pauli matrices
|
|
I removed this:
- , and the Pauli matrices generate the corresponding Lie group SU(2)
I don't see in what sense four matrices can "generate" an uncountable group, especially if they aren't even elements of that group. AxelBoldt 00:34 Apr 29, 2003 (UTC)
- By exponentiation. -- CYD
Looking at the replacement
- so the Pauli matrices are a representation of the generators of the corresponding Lie group SU(2).
I think I see the source of my confusion. We are not talking about generators in the sense of group theory, but rather "infinitesimal generators" of a Lie group, i.e. the elements of its Lie algebra. This should be clarified somewhere. So what we are really saying is that σ1,σ2 and σ3 form an R-basis of the Lie algebra su(2) of all Hermitian 2x2 matrices with trace 0, is that correct?
Also, the above link to group representation is misleading, since we are really representing a Lie algebra, not a group. I'll try to weave that into the article. AxelBoldt 20:02 Apr 29, 2003 (UTC)
- That sounds right to me. -- CYD