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1) show that the color factor Vqiqj = ~ (PEX - ~) , where PEX is a color exchange operator with the property that pJ;;X = I I for states symmetric in color exchange and PEX -1 for states an tisy III metric in color exchange. = 1.. 2. 1i\' color factors for the following quark-antiquark, quark-quark, and tlne qll ,trk states: (qq)[l], (qq)[S]' (qq)[3·], (qq)[6]' (qqq)[1], and (qqq)rsJ . 3. 4. Compute the color factors illustrated in Fig. 1. 5. 18) corresponds to an efrect of order 0',2. 6. 8). E.

1. 5. se ill QED. t a definite place in space. It is diffusely spread out due to gluon emi ss iOIl a nd absorption. As one increases the Q2 of the incoming gluon probe, I,h r by looking at smaller and smaller spatial distances, it becomes less likely to find the "charge" (red in Fig. u; Feynman diagram techniques with a coupling g. defined according to then the correct procedure is to simply replace a. by the effective couplill tJ; a. 18). By this procedure one automatically incorporates a n itp propriate infinite set of diagrams into each calculation.

Q2) becomes large and presumably confines quarks within hadrons. (Q2) takes a bit of getting used to. In QED it is easy to define what one means by the charge of an electron e. It is related to the large distance behavior of the electric potential (Thomson limit). (Q2) cannot be calculated by perturbation theory. (JJ2). 14) It, however, does not matter which point JJ one chooses. If one chooses instead the point fi then the two couplings are related (to lowest order) by _(1 2) - alog(Q2 /JJ 2) = (1_2) - alog(Q2/fi2), a.

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