[en] We investigate supersymmetry in one-dimensional quantum mechanics with point interactions. We clarify a class of point interactions compatible with supersymmetry and present N=2 supersymmetric models on a circle with two point interactions as well as a superpotential. A hidden su(2) structure inherent in the system plays a crucial role to construct the N=2 supercharges. Spontaneous supersymmetry breaking due to point interactions and an extension to higher N-extended supersymmetry are also discussed

[en] We investigate N-extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities. For any integer n, N=2n supercharges are explicitly constructed and a class of point singularities compatible with supersymmetry is clarified. Key ingredients in our construction are n sets of discrete transformations, each of which forms an su(2) algebra of spin 1/2. The degeneracy of the spectrum and spontaneous supersymmetry breaking are briefly discussed

[en] It is shown that any compactified closed string theory on an abelian orbifold is equivalent to that on a torus if the rank of the gauge symmetry of strings on the orbifold is equal to the dimension of the orbifold. Our proof clarifies the correspondence of operators as well as states between two theories. (author)

[en] It is shown that cocycle factors, which appear in vertex operator representations of affine Kac-Moody algebras or in compactified closed string theories on tori and/or orbifolds, have a simple geometrical meaning and that multiplying vertex operators by cocycle factors is equivalent to modifying commutation relations for zero modes. The origin of cocycle factors is revealed in the second quantized picture. (orig.)

[en] Working in a Hamiltonian formulation with A₀ = 0 gauge and also in a path integral formulation, we show that the vacuum wave functional of the four-dimensional pure Yang-Mills theory has the form of an exponential of a three-dimensional Yang-Mills action. This result implies that vacuum expectation values can be calculated in Yang-Mills theory but one dimension lower than the original theory. Our analysis reveals that this dimensional reduction results from the stochastic nature of the theory. (author)

[en] We study string theory on orbifolds in the presence of an antisymmetric constant background field in detail and discuss some of the new aspects of the theory. It is pointed out that the term with the antisymmetric background field can be regarded as a topological term like a Chern-Simons term. Detailed analysis in the operator formalism shows that orbifold models with topologically nontrivial twists exhibit various anomalous behavior: Zero-mode variables obey nontrivial quantization conditions. Coordinate transformations which define orbifolds are modified at quantum level. Wave functions of twisted strings in general acquire nontrivial phases when they move around non-contractible loops on orbifolds. Zero-mode eigenvalues are shifted from naively expected values, in favor of modular invariance. (orig.)

[en] We show that a wide class of supersymmetric theories, which includes N=1/2 supersymmetry, is obtained by use of a local Nicolai mapping. (author)

[en] We study cocycle properties of vertex operators and present an operator representation of cocycle operators, which are attached to vertex operators to ensure the duality of amplitudes. It is shown that this analysis makes it possible to obtain the general class of consistent string theories on orbifolds. (author)

[en] It is pointed out that symmetries between twisted and untwisted strings can appear in string theories on asymmetric orbifolds. The conditions that such symmetries appear are discussed. Examples of asymmetric Z₂- and Z₃-orbifold models are given. (author)

[en] Radiative corrections for the ground-state energy of the charged Dirac particle in a static uniform magnetic field are studied. Calculations of the one-loop diagram show that behaviors in the strong magnetic field depend on the type of the interactions. Improvement of the one-loop results is also discussed. (author)