From: goldenfieldquaternions@gmail.com   
      
   The anti-screening effect of color charge does result in this   
   inverted runn= ing coupling. What this does mean is that very high   
   energy QCD is reasonabl= y tractable. This conforms to a usual   
   situation that scattering states can = be computed well enough, but   
   bound states are tough.   
      
   As sqrt{s} --> 0 the number of diagrams blows up and they all   
   contribute eq= ually. In a sense the answer to the question of how   
   many gluons is "infinit= e." That is of course bad. That is where   
   lattice gauge theory comes in, whi= ch provides a cut off in diagrams   
   by a cut off in the size of the numerical=   
    lattice. Scaling the size of the lattice provides this low energy   
    renormal=   
   ization group flow.   
      
   LC   
      
   On Sunday, June 18, 2017 at 8:13:47 PM UTC-5, Gregor Scholten wrote:   
   > James Goetz  wrote:   
   >   
   > > Gluons bond quarks into baryons (i.e., protons and neutrons).   
   >   
   > More precisely, strong interaction binds quarks into baryons. Or   
   > in other words: gluons fields, i.e. fields of which gluons are field   
   > quanta (like photons are of the electromagnetic field), bind quarks   
   > into baryons. Using perturbation theory to calculate transition   
   > amplitudes caused by this strong interaction, one can say that   
   > quarks "exchange virtual gluons". More precisely: in perturbation   
   > theory, one uses the S-matrix to do calculations, and terms in the   
   > S-matrix can be graphically depicted by Feynman diagrams, with inner   
   > lines that are related to virtual particles.  In lowest order of   
   > perturbation theory, there is one inner gluon line between two   
   > quarks. In higher orders, there are higher numbers of inner lines.   
   >   
   > Sad to say, strong interaction contradicts one core aspect of   
   > perturbation theory, namely that higher orders yield lower contributions   
   > to transition amplitudes. For other interactions, like weak interaction   
   > or electromagnetic interaction, the main contributions come from   
   > lowest order, but strong interaction is that strong that all orders   
   > of perturbation theory yield comparable contributions. Take e.g.   
   > electromagnetic interaction: there, the coupling constant is 1/137,   
   > yielding a factor (1/137)^n for the n-th order, but for strong   
   > interaction, the coupling constant is approximately 1. So, Feynman   
   > diagrams with one inner gluon line contribute as much as diagrams   
   > with 2, 10 or 100 inner gluons lines.   
   >   
   > Therefore, perturbation theory is not a very appropriate method to   
   > describe strong interaction. A more appropriate approach is Lattice   
   > Gauge Theory.  This approach, however, does not yield virtual   
   > particles (gluons for strong interaction) as interaction intermediators.   
      
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