Quarks: Confinement Issues & Free Particles

Bready
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I'm struggling to get to grips with the idea that quarks cannot be observed as isolated particles due to confinement and yet existed as free particles during an early epoch after the big bang. Surely quarks aren't actually confined if they can exist at high enough energies.

In fact aren't these:

http://en.wikipedia.org/wiki/Quark-gluon_plasma

observations of free quarks? How is confinement being violated in these cases?
 
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You can't be too strict on your definition of "free". Is an electron in a metal, moving around on in the conduction band "free"? Well it can move around yes, but it is still subject to the potentials around it. Same with the QGP, they're not free in the sense that there is one particle, subject to no external influence. They are just compressed so much that there is no distinguished boundaries of the "baryons" everything overlaps and so can move as a plasma/soup.
 
Well you can compare this (i think) with aysompotic freedom of QCD, at high momentum transfer, quarks are "almost" free, the coupling decreases as energy scale increases. This is why quark-gluon plasma can occur.
 
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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