Matter & Anti-Matter: Why Do Particles Group in Matter?

mathfeel
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Is there any fundamental principle that explains why, for example, (up q, down q, and electron) are in the same group which we "happened" to call "matter", but not say (up q, down q, and positron)?

Because in the latter case, the world would consists of proton, neutron, and position and atoms would not form.
 
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I believe the thought goes like this: Matter and antimatter are created in equal amounts, therefore the world should not exist since the two should annihilate into energy once again. However, some effect in the early universe is thought to change this by breaking the CP (Charge Parity) symmetry. There is however no such effect observed that are strong enough to account for the huge surplus of matter. But if we for the moment accept that something caused this (for example a CP violation effect in the strong force), this would explain why the electron, and the up and down quarks make up our universe.
 
kaksmet said:
I believe the thought goes like this: Matter and antimatter are created in equal amounts, therefore the world should not exist since the two should annihilate into energy once again. However, some effect in the early universe is thought to change this by breaking the CP (Charge Parity) symmetry. There is however no such effect observed that are strong enough to account for the huge surplus of matter. But if we for the moment accept that something caused this (for example a CP violation effect in the strong force), this would explain why the electron, and the up and down quarks make up our universe.

I get that, but why did that CP-breaking process, whatever it might be, put (up, down, electron) into one group, called matter, which become dominated later and (anti-up, anit-down, positron) into another? Couldn't some other combination (up, down, POSITRON) be the dominate group instead?
 
There is one reason why one cannot mix the particles arbitrarily. Grouping fermions into so-called generations one gets (omitting anti-particles)

1st gen.:
- electron
- electron neutrino
- up-quark, down-quark

2nd gen.:
- myon
- myon neutrino
- s-quark, c-quark

3rd gen.:
- tau
- tau neutrino
- t-quark, b-quark

Within each generation certain charges must add up to zero in a non-trivial way (the counting is difficult e.g. due to three colors for the quarks and the weak isospin). w/o this property the standard model would have a gauge anomaly in the chiral electro-weak sector. Afaik gauge-anomalies mean that the quantized theory is mathematical inconsistent.
 
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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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