Selected Topics On QCD First Principle Computation And Spontaneous Symmetry Breaking

Quantum Chromo Dynamics as the fundamental theory that describes the strong in-teraction is always followed with interest by scientists. Because of its non-perturbativebehavior at low energy, to do calculations of low energy strong interaction process wasdifcult. Spontaneous symmetry breaking is the basic problems of quantum field theo-ry, the researches of Symmetry and its spontaneous Breaking could guide us proceedingthe theoretical physics. This thesis concerned about two of the non-perturbative spon-taneous symmetry breaking problem in QCD: the one is spontaneous Chiral symmetrybreaking; the other one is spontaneous Isospin symmetry breaking. For spontaneousChiral symmetry breaking, a very important character is the non-zero quark self ener-gy. In the past few years, our group performed QCD first principle calculations andderived quark self energy dependent Gauge invariant Non-local Dynamical quark mod-el(GND model) and its action, then derived all p6order’s coefcients of the efectivechiral lagrangian for pseudoscalar mesons due to the low energy expansion. It is wellmatched with experimental dates, then implies that quark self energy’s efect is impor-tant at low energy scale. Now we want to free of the low energy expansion, discusssome momentum dependent behavior of physical quantities, check the efects of quarkself energy or spontaneous Chiral symmetry breaking at higher energy scale. This thesiscalculated all three line vertices, and proved the Ward-Takahashi identity, validated theself-consistency of GND model. Then we calculated current-current correlators and ex-tracted the p4order’s coefcients of efective chiral lagrangian, most of these results arematch well. We also performed the large q2expansion to the correlators and comparedwith the operator product expansion method. Then we calculated some pion distributionamplitudes(PDAs), show that the parameter u is just the standard Feynman parameter.In the chiral limit, we find that with the exception of the contributions at two end-points,all PDAs are flat-like form, the corrections witch deviate PDAs from flat-like forms areall come from non-zero pion mass and quark current mass, the first order correctionsgive the concave asymptotic form, this result is also valid for any type of chiral quarkor NJL-like models. The results of a variety of comparison are good or not good, if ourcalculation was correct, it implies that quark self energy can play a very important ef-fect, but can not describe all problems perfectly. For the spontaneous Isospin symmetry breaking of QCD in the strong magnetic field, we researched order parameter’s con-densation based on first principle, point out that the direct calculations from generatingfunctional is very hazardous. The correct way is to calculating the efective action toinclude all possible vacuum. We held a counter example to show that the original Vafa-Witten’s proof is questionable, and propose to Amending the Vafa-Witten theorem.