Talk:Wigner's classification

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Unbounded continuous operators? Where I come from, continuous operators are bounded.

Charles Matthews 08:36, 5 Feb 2004 (UTC)

also, are we really using this method to find the unitary irreps of Poincare? a noncompact group does not have finite dimensional unitary reps. and Poincare is noncompact, and it looks like these are finite dimensional irreps, thus they cannot be unitary. i am going to delete the word unitary, and the word continuous, according to Charles' comment above._Lethe 21:49, 8 Mar 2004 (UTC)

[edit] unitary or not?

at some time in the past, i mentioned on this talk page that I don't think the irreps of Poincaré should be unitary. So I deleted that word from the article. Someone recently added the word back in, and it seems that in Wigner's original paper, he does mention unitary irreps. However, I still think it's true that noncompact groups do not have finite dimensional unitary irreps. So what's the deal? Maybe the idea is just that the induced rep of the little group is unitary? Lethe

I guess it's not clear from the article but the irreps here are infinite dimensional (except for the vacuum). Phys 19:21, 1 Aug 2004 (UTC)

Also, the "little groups" (stabilizers) are spin(3) and the double cover of SE(2). The first is compact (but the resulting FULL Poincaré rep is still infinite dimensional since we'd have to integrate over all energy-momenta on the mass shell) and the latter, while noncompact, still admits finite dimensional unitary reps (the continuous spin rep is infinite dimensional, though)! Phys 19:27, 1 Aug 2004 (UTC)

[edit] Nonnegative energy

I am a mathematician, so the definition in terms of "nonnegative energy" makes absolutely no sense to me. Also phrases like "sharp mass eigenvalues". What do they mean mathematically? Surely there is room for both kinds of explanation (physical and mathematical). - 72.57.120.3 05:36, 20 September 2006 (UTC)