Non-Perturbative Effects In Quantum Chromodynamics And Beyond

The non-perturbative aspects of quantum field theory are explored in which the cen-tral ingredients are the symmetry principles,the polology of matrix elements,and the renormalization that takes account of radiative corrections.It is therefore applicable to strong interaction systems where the composite particles are made up of confined quarks and gluons,the coupling among which is large enough at low energy to defy any perturbative calculation.As a special problem,non-perturbative proof is presented of a generalized version of Goldstone theorem,where the Lagrangian conserves an approximate SU(3)chiral symmetry,that both quark masses and electromagnetism make contributions to the masses of spinless particles of pseudoscalar octet.It is shown that apart from what comes in the form of some projections of a two-body Bethe-Salpeter amplitude for which the photon lines like the gluon ones are all internal in the case of neutral pseudo-Goldstone bosons,the charged pseudoscalar mesons receive additional contributions that may be expressed in terms of the axial-vectorial projection of a three-body Bethe-Salpeter amplitude with an extra external photon line.It is widely acknowledged that effective field theories that successfully describe the relevant degrees of freedom such as the Goldstone bosons are the way they are,because they are constructed in consistence with the general principles of relativity,quantum mechanics,and the assumed symmetries.As a generalization of the methods first used in an understanding of the attributes and behaviour of pions and nucleons,it is to utilize the effective field theory approach to study the properties of the axion,which is the corollary of the strategy to solve the problem of parity and time-reversal violation by non-perturbative effects in quantum chromodynamics.In particular,with the s as well as the u and d quarks regarded as relatively light we derive formula for the mass of the axion;a rough estimate of the rate for its dominant decay mode at low energy is also carried out.The work is complete and consistent in itself.