Helicity Amplitude Analysis Method And Gluon Generating Functional

In this thesis, firstly a thorough review is made on the covariant helicity amplitude analysis method. Poincare group, Dirac representation, amplitude analysis method. In addition, the amplitude perturbation analysis are carefully discussed to a practical reaction process, J/ψ→γπ~+π~-. Further, the Bargman-Wigner (B-W) Equations are resolved rigorously and the explicit expression of relativistic wave functions for high spins in momentum representation are derived. Moreover, based on the work of Prof. T. D. Lee, the pure gluon generating functional is obtained through the sea quark's contribution. To be specific, the main works of this thesis are as follows.Confirming the existence of gluon-ball is an important criterion for testing Quantum Electrodynamics (QCD). In order to satisfy the demand of BES in the Institution of High Energy Physics (IHEP) to analysis the experimental data, theoretically, it is indispensable to work out a reliable and practical analysis method. The preferred method is helicity amplitude analysis, which is incomplete in classical theory. For example, S. U. Chung's Spin Formalism is not absolutely covariant, and therefore it is not suitable for high energy particle process. Hence it is necessary to establish a covariant theory. Moreover, to expand its application, partial wave amplitude and phase-shift analysis should also be comprised in the theory.Consequently, the helicity amplitude analysis method is firstly systemized, S. U. Chung's theory is modified and the relativistic helicity amplitude analysis method is established. In this part, method of partial waves and phase-shift analysis are brought into the theory. At the same time, Poincare group theory and composition, Dirac representation and the construction of two-particle states are studied systematically.Secondly, to study particles with arbitrary integral spin and half-integral spin, the relativistic wave functions (including both the positive energy and the negative energy solutions) for arbitrary integral and half-integral spins in momentum representation are developed from the B-W equations. Starting from low spins, the general wave functions for arbitrary integral and half-integral spins are deduced in a step-by-step way. That is: the wave functions for an arbitrary integral spin n are expressed by n e_λ~μ's (the wave functions of spin 1) coupled by C.G coefficients, the wave functions for an arbitrary half-integral spin n+1/2 are expressed by the wave functions of spin n and the Dirac spinors u_γ and v_γ coupled by C.G coefficients, in which only the coupling correspond to the maximum possible spin is kept.Thirdly, on the basis of the T. D. Lee wave equation-QCD Schrodinger equation, Prof. T. D. Lee has given the rigorous path integral expression of QCD generating functional, from which all the necessary green functions for the harmonic process are obtained and calculated by path integral techniques. With the contribution of sea quarks, the generating functional of pure gluons is derived, which providing the theoretical basis for gluon-ball studies.Fourthly, since the experimental discovery of shape transition and halo phenomena, the study of exotic nuclei has become a very challenging topic in nuclear physics. RMF theory has been applied with considerable success to the quantitative description of nuclear properties in the ground states and to the prediction for the shape transition and halo in the excited states, it is also interesting to give theoretical prediction for shape transition and halo in realistic nuclei with RMF model. In this chapter, we apply RMF theory to investigate the shape transition and halo in some exotic nuclei.