Can Elementary Particles be related with irreducible representation?

Clandestine M
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Hi,

I am quite naive in Particle Physics, and I have a question that

Can Elementary Particles be related with irreducible representation?


Could we say scalar, vector, and spinor are irreducible representation of SO(3)?


Thanks a lot! I also wish I could have some reference on this topic.
 
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Thanks a lot! Internal symmetry should also be considered. In the beginning part of this article, only Poincare' Symmetry for classification has been mentioned.
 
And the difference of classification of Boson and Fermion?
 
... always bearing in mind that wikipedia should be treated only as a starting point for further searches.
From the links provided you should be able to find the rest that you are looking for.
 
Toponium is a hadron which is the bound state of a valance top quark and a valance antitop quark. Oversimplified presentations often state that top quarks don't form hadrons, because they decay to bottom quarks extremely rapidly after they are created, leaving no time to form a hadron. And, the vast majority of the time, this is true. But, the lifetime of a top quark is only an average lifetime. Sometimes it decays faster and sometimes it decays slower. In the highly improbable case that...
I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...

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