Instantons in QCD: Theory and application of the instanton liquid model

Abstract

Numerical and anaytical studies of the instanton liquid model have allowed the determination of many hadronic parameters during the last 13 years. Most part of this thesis is devoted to the extension of the analytical methods. The meson correlation (polarization) functions are calculated in the instanton liquid model including dynamical quark loops. The correlators are plotted and masses and couplings of the $σ$, $ρ$, $ω$, $a1$ and $f1$ are obtained from a spectral fit. A separated analysis allows the determination of the $η'$ mass too. The results agree with the experimental values on a 10\% level. Further I give some predictions for the proton form factors, which are related to the proton spin (problem). A gauge invariant gluon mass for small momenta is also calculated. At the end of the work some predictions are given, which do not rely on the instanton liquid model. A gauge invariant quark propagator is calculated in the one instanton background and is compared to the regular and singular propagator. An introduction to the skill of choosing a suitable gauge, especially a criterium for choosing regular or singular gauge, is given. An application is the derivation of a finite relation betweewn the quark condensate and the QCD scale $Λ$, where neither an infrared cutoff nor a specific instanton model has been used. In general the instanton liquid model exhibits an astonishing internal consistency and a good agreement with the experimental data.