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6

Let me first make a general remark about internal symmetry groups, unrelated to our problem of the correct symmetry group for QCD. The symmetry must act on Hilbert space as a unitary operator for the conservation of probability. Now let us turn to the strong interaction. The most important experimental facts were that Observed hadron spectrum was ...

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Part of your confusion here probably comes from your notation. Usually we reserve the index $\mu$ for spacetime. The generators of $SU(N)$ are more commonly labelled with Latin indices $t^a$. See for example here. We can split the amplitude into two parts, according to whether they concern color or kinematics. You are just interested in the color part. Each ...

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I too see this often, @QMechanic. See, for example, Griffiths, Introduction to Elementary Particles, pg 47. By this they mean that the time it would take for signals to cross the 'length' of a typical hardon is much longer than the time it takes for a top (truth!) quark to decay. Since we assume cuasility, we cannot have an interaction which propagats ...

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Antiquarks can be distinguished from quarks, so you only need to antisymmetrize two at a time. That's no problem, and even if you had 3 quarks it wouldn't be. Furthermore, you only need the total state to be antisymmetric. You could have antisymmetry in space, symmetry in spin and symmetry in color, and the whole thing would be antisymmetric. (Like how you ...

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In simple terms QCD as a "background" usually refers to LHC research where hadronic jets create a lot of particles that clutter up the results you're trying to see. I think it has become a slang term and the use is discouraged. ABCD method is a tool used to separate the particles of interest (signal) from the "other stuff" (background) made by the jets. ...

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Maybe I've figure out something about that. QCD is an asymptotically free theory, so while for the high energy regime, consider the perturbative method, expanding around $g=0$, is perfectly consistent, for the low energy scales this approach becomes useless. An attempt to manage this problem, is to consider an expansion in terms of the parameter ...

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I) Bosonic part: When we Wick-rotate, it is more natural to use sign convention $$\tag{1} \eta_{\mu\nu}~=~{\rm diag}(-1,+1,+1,+1)$$ for the Minkowski (M) metric, and $$\tag{2} \delta_{\mu\nu}~=~{\rm diag}(+1,+1,+1,+1)$$ for the Euclidean (E) metric. Here we will use Greek indices $\mu,\nu=0,1,2,3$, to denote spacetime indices, and Roman indices ...

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