D = 2, N = 2 generalized Wess-Zumino theory is investigated by the dimensional reduction from D = 4, N = 1 theory. For each solitonic configuration (i, j) the classical static solution is solved by the Hamilton-Jacobi method of equivalent one-dimensional classical mechanics. It is easily shown that the Bogomol'nyi mass bound is saturated by these solutions and triangular mass inequality

We investigate a two-dimensional N = 2 supersymmetric model which consists of n chiral superfields with Kähler potential. When we define quantum observables, we are always plagued by operator ordering problem. Among various ways to fix the operator order, we rely upon the supersymmetry. We demonstrate that the correct operator order is given by requiring the super-Poincaré algebra by carrying out the canonical Dirac bracket quantization. This is shown to be also true when the supersymmetry algebra has a central extension by the presence of topological soliton. It is also shown that the path of soliton is a straight line in the complex plane of superpotential W and triangular mass inequality holds. One half of supersymmetry is broken by the presence of soliton.

We investigate an operator ordering problem in two-dimensional N = 1 supersymmetric model which consists of n real superfields. There arises an operator ordering problem when the target space is curved. We have to fix the ordering in quantum operator properly to obtain the correct supersymmetry algebra. We demonstrate that the super-Poincaré algebra fixes the correct operator ordering. We obtain a supercurrent with correct operator ordering and a central extension of supersymmetry algebra.

The cosmological observation indicates that the effective equation of state parameter w ef f varies with z: It changes from w ef f > −1 to w ef f < −1 at z ∼ 0.2. We investigate under which condition it exhibits such behaviors based on the fivedimensional braneworld scenario. It is possible in the model with or without an energy exchange between the four dimensional universe and the fifth dimension. However the curves of w ef f are quite different between the two cases.

We will show that 2-dimensional N = 2-extended supersymmetric theory can have solitonic solution using the Hamilton-Jacobi method of classical mechanics. Then it is shown that the Bogomol'nyi mass bound is saturated by these solutions and triangular mass inequality is satisfied. At the end, we will mention domain-wall structure in 3-dimensional spacetime.