Talk:Wigner's classification

message: Unbounded continuous operators? Where I come from, continuous operators are bounded.
Charles Matthews 08:36, 5 Feb 2004 (UTC)
thread_title: Misc 

message: 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)
replies: text: 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)

text: You mean the joint 1948 one, Bargmann, V., & Wigner, E. P. (1948). Group theoretical discussion of relativistic wave equations. Proceedings of the National Academy of Sciences of the United States of America, 34(5), 211? Why?  All right, if you thought this is warranted supplementary material, I could link it, for pedagogy. Cuzkatzimhut (talk) 16:16, 13 June 2014 (UTC)
thread_title:  unitary or not? 

message: The content of the "note" at the bottom about tachyons and off-shell particles are misleading.  Tachyonic solutions and virtual states do not furnish irreps of the Poincare group, and so leaving them out is "correct".  The paragraph makes it sound like the classification is incomplete.  I suggest removing it entirely, or shortening it.
TriTertButoxy (talk) 12:37, 24 July 2015 (UTC)
thread_title:  The "note" is slightly incorrect 

message: Very technical, as it should be, but doesn't define stuff. 84.226.185.221 (talk) 12:27, 10 October 2015 (UTC)
thread_title:  Article too brief 

message: :These two actions can be combined in a clever way using induced representations to obtain an action of P on L^2(M) that combines motions of M and phase multiplication.
I would love to see the explicit formula for this. So far, I have been too lazy to work it out or look it up. 178.39.122.125 (talk) 10:16, 16 October 2016 (UTC)
thread_title:  Fuill out formula 

message: These references really spell it out, very mathematically but with all the physics.
(1) George Mackey, Unitary Group Representations in Physics, Probability and Number Theory, 1978.
(2) Shlomo Sternberg, Group Theory and Physics, 1994, Section 3.9. (Wigner classification)
(3) Wu-Ki Tung, Group Theory in Physics, 1985, Chapter 10. (Representations of the Lorentz group and of the Poincare group; Wigner classification)
178.39.122.125 (talk) 10:37, 16 October 2016 (UTC)
replies: text: I added those to the article. Thanks for the new section on massive scalar fields. YohanN7 (talk) 11:02, 17 October 2016 (UTC)
thread_title:  References