Talk:Particle physics and representation theory

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There are a number of items that I put on this page that I'm not 100% sure about. For example, I'm not sure exactly what Wigner's Theorem is or how it fits in. I also may be misstating the facts about color and flavour symmetry, and I may be oversymplifying the classification of representations of the Poincare group. Steve

What does it mean for a particle to "lie in" a representation of G? A representation is just a homomorphism from G to the Hilbert space, so is this saying that the action of G on the vector representing the particle is nontrivial, or something else? - 72.58.19.66 00:58, 8 May 2006 (UTC)

I think the "lie in" is clearer now. Steve

second the comment below re clean-up required. a representation is a homomorphism from G to the, in this case, bounded operators on a Hilbert space. "lie in" doesn't seem like very good language. in algebra, it is called the orbit of a given |p₀>. Mct mht 05:21, 8 February 2007 (UTC)

[edit] sloppy

This article is very vague about a number of points and I would recommend that it be put on status to require "clean up" by an expert. The most pressing need is the need for a few equations to eliminate some of the hand waving. There are also factual errors in the text. For example, SU(3) is the gauge of the strong force, but SU(2) (left) is the gauge of the weak force. They are distinct gauge groups. SU(2) (left) is weakly violated (and hence is only an approximate symmetry; SU(3) is an exact symmetry.

I don't understand those "factual errors". Yes, SU(2) (left) is the gauge of the weak force, but does the article say (or imply) otherwise? The article does say that color SU(3) is an example of an exact symmetry, which is true. So exactly which sentence(s) of the article are you disputing? Steve

[edit] which postulate

From the first paragraph, "This postulate states that each particle is an irreducible representation of the symmetry group of the universe." To which postulate is this referring? Mathchem271828 05:35, 6 January 2007 (UTC)