Talk:Generalizations of Pauli matrices

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 Field:  Algebra

Traceless ?[edit]

I suggest the following correction

[The generalized Gell-Mann matrices are Hermitian and traceless]


[The generalized Gell-Mann matrices are Hermitian and (save h1d) traceless]

Duplicated section?[edit]

It looks to me like the section titled "A non-Hermitian generalization of Pauli matrices" describes exactly the same operators (or perhaps a transpose thereof) as the section titled "A unitary generalization of the Pauli matrices". Am I missing something here?

Dstahlke (talk) 14:19, 26 October 2012 (UTC)

Not much; the article is a disorganized mess. It should start by organizing the grading issues, the way they were laid out in the original reference, Patera, J.; Zassenhaus, H. (1988). "The Pauli matrices in n dimensions and finest gradings of simple Lie algebras of type An−1". Journal of Mathematical Physics. 29 (3): 665. Bibcode:1988JMP....29..665P. doi:10.1063/1.528006. , which is oddly missing here. Sylvester did it all, of course, in the 1880s, but skipping the modern perspective and obscuring the facts you mention makes the article useless. I fear you must intervene. Cuzkatzimhut (talk) 15:08, 26 October 2012 (UTC)

Textbook language?[edit]

In this article one can read "Clearly the family specified by above consists of unitary matrices. To see that they indeed generalize the Pauli matrices, in some sense, we compute...". "Clearly"? (What about telling us ignorants why it is so clear?!) And who are the "we" that compute? --Episcophagus (talk) 00:56, 2 November 2012 (UTC)

I agree with your distaste of the false pedagogy of that section, and, as I argued above, it would improve the article by completely disappearing. I adduced the standard one-liner summary of it in the previous section. If you are familiar with unitarity, which i wikilinked, now, the unitarity of these sylvester matrices should be self-evident. "Clearly" might sound condescending, but it is a salutary signal that there is nothing deep involved: one simply writes its articulation on a line with an equal sign, and collapses the orthonormal vectors v that person uses. Now, why she/he switches notation for the roots of unity to ξ instead of the prior σ, and why he/she references that idiosyncratic obscure last reference, we might never know. It would be a kindness to the reader to have that section go.Cuzkatzimhut (talk) 14:56, 2 November 2012 (UTC)