Abstract:
Hyperon non-leptonic weak decay amplitudes are studied in the chiral perturbation theory. The weak interaction vertices caused by the four quark operators are substituted by the products of the hadronic currents and by the phenomenologically introduced weak Hamiltonian of hadron operators. Our study suggests the improvement of the theoretical prediction for the weak decay amplitudes.

Abstract:
Hyperon non-leptonic weak decay amplitudes are studied in the chiral perturbation theory. We employ the low energy effective weak Hamiltonian which contains the perturbative QCD correction. To include the non-perturbative QCD effect, quark currents of the effective Hamiltonian are substituted with hadronic currents which are color singlet and are derived by the chiral perturbation theory. We find that the amplitudes caused by the product of hadronic currents are small. It reproduce the small amplitudes of $\Delta I=3/2$, which are derived by the strong interaction correction.

Abstract:
The Bethe--Salpeter equation for the pion in chiral symmetric models is studied with a special care to consistency with low-energy relations. We propose a reduction of the rainbow Schwinger--Dyson and the ladder Bethe--Salpeter equations with a dressed gluon propagator. We prove that the reduction preserves the Ward--Takahashi identity for the axial-vector current and the PCAC relation.

Abstract:
We study effects of nonlocality in the nuclear force on the G-matrix elements for finite nuclei. Nuclear G-matrix elements for $\O16$ are calculated in the harmonic oscillator basis from a nonlocal potential which models quark exchange effects between two nucleons. We employ a simple form of potential that gives the same phase shifts as a realistic local nucleon potential. The G-matrix elements calculated from the nonlocal potential show moderate increase in repulsion from those derived from the local potential.

Abstract:
Nonmesonic weak decays of the A=4, and 5 hypernuclei are studied. The short range parts of the hyperon-nucleon weak interactions are described by the direct quark (DQ) weak transition potential, while the longer range interactions are given by the $\pi$ and $K$ meson exchange processes. Virtual $\Sigma$ mixings of the coherent type are found to give significant effects on the decay rates of $^4_{\Lambda}{\rm He}$. A large violation of the $\Delta I = 1/2$ rule is predicted in the J=0 transition amplitudes.

Abstract:
Nonmesonic weak decays of s-shell hypernuclei are analyzed in microscopic models for the Lambda N to NN weak interaction. A scalar-isoscalar meson, sigma, is introduced and its importance in accounting the decay rates, n/p ratios and proton asymmetry is demonstrated. Possible violation of the Delta I=1/2 rule in the nonmesonic weak decay of Lambda is discussed in a phenomenological analysis and several useful constraints are presented. The microscopic calculation shows that the current experimental data indicate a large violation of the Delta I=1/2 rule, although no definite conclusion can be derived due to large ambiguity of the decay rate of {^4_Lambda H}.

Abstract:
The meson(K and $\pi$) exchange currents for the hypernuclear magnetic moments are calculated using the effective Lagrangian method. The seagull diagram, the mesonic diagram and the $\Sigma^0$-excitation diagram are considered. The $\Lambda$-N exchange magnetic moments for the ${}^5_{\Lambda}He$, ${}^6_{\Lambda}He$ and ${}^6_{\Lambda}Li$ are calculated employing the harmonic oscillator shell model. It is found that the two-body correction is about -9% of the single particle value for ${}^5_{\Lambda}He$. The $\pi$ exchange current, induced only in the $\Sigma^0$-excitation diagram, is found to give dominant contribution for the isovector magnetic moments of hypernuclei with A=6.

Abstract:
The Wilsonian renormalization group (RG) method is applied to finite temperature systems for the study of non-perturbative methods in the field theory. We choose the O(N) linear sigma model as the first step. Under the local potential approximation, we solve the Wilsonian RG equation as a non-linear partial differential equation numerically. The evolution of the domain is taken into account using the naive cut and extrapolation procedure. Our procedure is shown to yield the correct solution obtained by the auxiliary field method in the large $N$ limit. To introduce thermal effects, we consider two schemes. One in which the sum of the Matsubara frequencies are taken before the scale is introduced is found to give more physical results. We observe a second order phase transition in both the schemes. The critical exponents are calculated and are shown to agree with the results from lattice calculations.

Abstract:
Decays of $\Lambda$ in nuclei, nonmesonic mode, are studied by using the $\Lambda N \to NN$ weak transition potential derived from the meson exchange mechanism and the direct quark mechanism. The decay rates are calculated both for the $\Lambda$ in symmetric nuclear matter and light hypernuclei. We consider the exchange of six mesons ($\pi, K, \eta, \rho, \omega, K^\ast$). The form factor in the meson exchange mechanism and short range correlation are carefully studied.

Abstract:
We study the O(N) symmetric linear sigma model at finite temperature as the low-energy effective models of quantum chromodynamics(QCD) using the Cornwall-Jackiw-Tomboulis(CJT) effective action for composite operators. It has so far been claimed that the Nambu-Goldstone theorem is not satisfied at finite temperature in this framework unless the large N limit in the O(N) symmetry is taken. We show that this is not the case. The pion is always massless below the critical temperature, if one determines the propagator within the form such that the symmetry of the system is conserved, and defines the pion mass as the curvature of the effective potential. We use a new renormalization prescription for the CJT effective potential in the Hartree-Fock approximation. A numerical study of the Schwinger-Dyson equation and the gap equation is carried out including the thermal and quantum loops. We point out a problem in the derivation of the sigma meson mass without quantum correction at finite temperature. A problem about the order of the phase transition in this approach is also discussed.