14 
NET FORCES IN QCD 
O EVISE What happens when two gluons meet? In most cases they just pass by each other without interacting. Two gluons couple difficult. In page 2, paragraph "Summary of what we have met until now” (near the end of the page), we found (in socalled timesymmetric representation): * = * = zero = * = zero = * = Page 2, fig 9 gives: The 2 gluons pass by each other. When another 2 gluons are allowed to emerge then the first 2 gluons and the last 2 can be allowed to merge and escape. There are 2 possibilities for this: and As argued 2 gluons merging is not a like thing to be but this gives rise to the rule * = * = * = * = The merging of 2 gluons with same upper colors and different lower colors always yields a glueball of the upper color. The merging of 2 gluons with same lower colors and different upper colors always yields a glueball of the lower color In space this might very well resemble the emerging of 4 gluons merging to 1 glu4on that immediately decays in 2 glueballs (ordinary glue1balls) emitted in opposite direction and with opposite spin. It is as if the 2 quarks go right through each other without interacting accompanied by the emerging of 2 glueballs at the point of coinciding. The 2 possibilities are: yields or Does * occur in nature and what is the outcome? In terms of colorshift this yields +2/6 * +2/6 = +2/6 +2/6 = 2/6 gluon and there are 3 of them: – , – and – . In the next figure the colors of the gluons are all determined by the colors of the quarks they couple to, except for the graypictured gluon D that is loose from quarks: it couples to gluons only. Can we find a definite value for the 2 colors of D? As far as the colors are concerned, any gluon can always couple to any other gluon. But if we take D as we get two rules:  *  = + (B and C merge to D) and  *  = + (D and A merge to E) which is the same rule. The colors then fit nicely. The other 2 solutions for D give according to the rules we know so far:  *  = + and  *  = + Then quark absorbs gluon +2/6 and becomes . Or quark absorbs gluon +2/6 and becomes . The colors don’t fit. But this is allowed in terms of colorshift. If the colorshiftapproach is right then all 3 possibilities for the colors of D are indistinguishable solutions and occur in superposition at D. If the colors are crucial and have to fit then is  *  = + and the other 2 solutions are invalid. It seems the reaction can decide between the 2 views, whether one should always follow the colorpaths precisely or that only the colorshifts count. Let’s try to construct a table of all possible gluongluonreactions. We have enough information now. When colors are decisive, a gluon at an intersection point of a row and a column is the product, the result of merging, of the most right gluon in the row and the most upper gluon in the column. For * we fill in . In QUATERNIONS (use the gluon table): * = ( j / i ) * ( j /i ) = i * j * i * j = k * k = 1 This is a colorless mesonic gluon, part of the time axis. The solution looks different from those obtained with the colorcircle.  For reasons of symmetry we fill in for * = * = .
This is the gluon multiplication table in timesymmetric representation. Of course there is a normal representation too. The lower colors shown in the scheme above are changed in their anticolors. Consider the meeting of 2 and 3 hadrons. (Mark the mesonic shift +3/6 and the “antimatter”shifts +1/6 and 1/6, introduced in page 3 of this storyline, are left out in the table so far. Yet to be implemented.) NEXT PAGE Up CONTACT 
