Dirac's method which itself is for constrained Boson fields and particle systems is followed and developed to treat Dirac fields in light-front coordinates.
The generating functional for truncated Green functions which is lacking in the field theories, is introduced for the spinor electrodynamics. Such generating functional is shown to be excellent in expressing the scattering matrix and used to construct a formula for the latter. The method is also applicable in principle to other field theories.
An effective Hamiltonian including current-current coupling from the Global Color symmetry Model (GCM) is derived. Retardation effects are introduced by the factor R √ π e −R 2 τ 2 , instead of δ(τ) in the correlation kernel, from which the retardation gap equation with α − α coupling in the 3 P 0 vacuum is obtained. qq condensation of different retardation parameters R with or without the α − α term are calculated. The results show the effects of retardation, and indicate that the typical value of R is about 2 f m −1 at reasonable value ofqq condensation. And while taking typical value 1 fm −1 of R, the condensation qq 1 3 is about 13% larger than that with no retardation effect. With the α − α terms, the condensation qq 1 3 are about 17% larger than that without it for all values of the parameter R. This shows the retardation effects and the α − α terms are important for further studying in low region.
The Fermi–Yang Liming method is followed and developed to estimate new magic numbers in nuclei with a Woods–Saxon density function. The calculated results predict that the magic number next to 126 should be around 184 and 258.
The superdeformed bands in A ~ 190 region were systematically investigated to indicate the existence oi AI = 4 bifurcation in this region. The behavior of bifurcation was also discussed.
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