Academic Lecture: The dynamical generation of the mass gap and gluon confinement


Title: The dynamical generation of the mass gap and gluon confinement 
Speaker: Prof.Vahtang Gogokhia (WIGNER RCP) 
Time: 10:00AM, Apr.25th 2017 (Tuesday) 
Place: Theoretical Physics Division,319 
Abstract: The general scale parameter, having the dimensions of mass squared, in what follows- the mass gap, is dynamically generated by the self-interaction of massless gluon modesin the YM sector of QCD. It is introduced through the difference between the regularized full gluon self-energy and its value at some nite point. The role of the four-gluon point-like vertex is to be emphasized. We have shown how to preserve the ST identity forthe full gluon propagator when the mass gap is explicitly present in the corresponding SD equation of motion for it. The mass gap term dominates the structure of the full gluon propagator when the gluon momentum goes to zero. This makes it possible to accumulate/summarize all the severe IR singularities into full gluon propagator. Using the distribution theory, the dimensional regularization method, both complemented by the Picard theorem from the theory of functions of complex variable, we have shown that after the renormalization program is performed, only the simplest severe IR singularity (possible in four-dimensional QCD) survives. It explains why the potential between heavy quarks, "seen" by lattice simulations, is only linear one. For the rst time, we were able to analytically formulate the gluon con nement criterion in the gauge-invariant way. The mass gap approach to QCD sheds light on the scale violation at high energies in QCD.