Related papers: New features in supersymmetry breakdown in quantum…
Heisenberg-type higher order symmetries are studied for both classical and quantum mechanical systems separable in cartesian coordinates. A few particular cases of this type of superintegrable systems were already considered in the…
It is shown by analyzing the $1D$ Schr\"odinger equation that discontinuities in the coupling constant can occur in both the energies and the eigenfunctions. Surprisingly, those discontinuities, which are present in the energies {\it…
We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang-Mills theory. It gives a topological quantum model that has interesting and…
We formulate N-fold supersymmetry in quantum mechanical systems with reflection operators. As in the cases of other systems, they possess the two significant characters of N-fold supersymmetry, namely, almost isospectrality and weak…
A supercurrent superfield whose components include a conserved energy-momentum tensor and supersymmetry current as well as a (generally broken) R-symmetry current is constructed for a generic effective N=1 supersymmetric gauge theory. The…
We review a class of models of dynamical supersymmetry breaking, and give a unified description of these models.
We report a new type of supersymmetry, "N-fold supersymmetry", in one-dimensional quantum mechanics. Its supercharges are N-th order polynomials of momentum: It reduces to ordinary supersymmetry for N=1, but for other values of N the…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
Recently, it was observed that self-interacting scalar quantum field theories having a non-Hermitian interaction term of the form $g(i\phi)^{2+\delta}$, where $\delta$ is a real positive parameter, are physically acceptable in the sense…
We demonstrate the existence of a novel set of discrete symmetries in the context of N = 2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic…
In this chapter we treat the quantum damped harmonic oscillator, and study mathematical structure of the model, and construct general solution with any initial condition, and give a quantum counterpart in the case of taking coherent state…
Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, $C$-selfadjoint…
We show that a quantum-mechanical N=2 supersymmetry is hidden in 4d mass spectrum of any gauge invariant theories with extra dimensions. The N=2 supercharges are explicitly constructed in terms of differential forms. The analysis can be…
Supersymmetric quantum gauge theories are important mathematical tools in high energy physics. As an example, supersymmetric matrix models can be used as a holographic description of quantum black holes. The wave function of such…
We construct supersymmetric gauge theories with new mechanisms of dynamical supersymmetry breaking. The models have flat directions at the classical level, and different mechanisms lift these flat directions in different regions of the…
It is an interesting and open problem to trace the origin of the pseudospin symmetry in nuclear single-particle spectra and its symmetry breaking mechanism in actual nuclei. In this report, we mainly focus on our recent progress on this…
We discuss the properties of superintegrable Hamiltonian systems, in particular those that admit separation of variables in cartesian coordinates. We show that the superintegrability of such potentials is equivalent to the isochronicity of…
We present a clear and mathematically simple procedure explaining spontaneous symmetry breaking in quantum mechanical systems. The procedure is applicable to a wide range of models and can be easily used to explain the existence of a…
We study higher dimensional field theories with extra dimensions from a 4d spectrum point of view. It is shown that 4d mass spectra of spinor, gauge and gravity field theories are governed by quantum-mechanical supersymmetry. The 4d…
A model of gauge-mediated supersymmetry breaking is constructed in which the low-energy physics depends on a single dynamical scale. Strong coupling dynamics of gauge theories plays an important role, in particular through its effects on…