Related papers: Supersymmetrical Separation of Variables for Scarf…
We employ our new approach to non-relativistic supersymmetric quantum mechanics (SUSY-QM), (J. Phys. Chem. A 114, 8202(2010)) for any number of dimensions and distinguishable particles, to treat the hydrogen atom in full three-dimensional…
Originally developed in the context of quantum field theory, the concept of supersymmetry (SUSY) can be used to systematically design a new class of optical structures. In this work, we demonstrate how key features arising from optical…
We have constructed the quasi-exactly-solvable two-mode bosonic realizations of su(2) and su(1, 1) algebra. We derive the relations leading to the conditions for quasi-exact solvability of two-boson Hamiltonians by determining a general…
Quantum Hamilton-Jacobi Theory and supersymmetric quantum mechanics (SUSYQM) are two parallel methods to determine the spectra of a quantum mechanical systems without solving the Schr\"odinger equation. It was recently shown that the shape…
We generalize the SU(2|2) supersymmetric extended Hubbard model of 1/r2 interaction to the SU(m|n) supersymmetric case. Integrable models may be defined on both uniform lattice and non-uniform one dimensional lattices. We study both cases…
The perturbation method in supersymmetric quantum mechanics (SUSYQM) is used to study the spheroidal wave functions' recurrence relations, which are revealed by the shape-invariance property of the super-potential. The super-potential is…
A supersymmetric $Sp_{L}(6) \times U_{Y}(1)$ model (SUSY $Sp(6)$) is proposed as an extension of the standard electroweak model. The model is applied in a phenomenological study of $B^{0}_{d} \bar{B}^{0}_{d}$ mixing. It is found that the…
Supersymmetry (SUSY) of Hamiltonian dictates double degeneracy between a pair of superpartners (SPs) transformed by supercharge, except at zero energy where modes remain unpaired in many cases. Here we explore a SUSY of complete isospectrum…
We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the…
We analyze a set of three PT-symmetric complex potentials, namely harmonic oscillator, generalized Poschl-Teller and Scarf II, all of which reveal a double series of energy levels along with the corresponding superpotential. Inspired by the…
We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are…
We review the higher-order supersymmetric quantum mechanics (H-SUSY QM), which involves differential intertwining operators of order greater than one. The iterations of first-order SUSY transformations are used to derive in a simple way the…
We study the superpotentials, quantum parameter space and phase transitions that arise in the study of large N dualities between $\mathcal{N}=1$ SUSY U(N) gauge theories and string models on local Calabi-Yau manifolds. The main tool of our…
In the zoo of emergent symmetries in quantum many-body physics, the previously unrealized emergent spacetime supersymmetry (SUSY) is particularly intriguing. Although it was known that spacetime SUSY could emerge at the (1+1)d tricritical…
We propose a new mechanism of spontaneous supersymmetry breaking. The existence of extra dimensions with nontrivial topology plays an important role. We investigate new features resulting from this mechanism. One noteworthy feature is that…
The multidimensional N=4 supersymmetric quantum mechanics (SUSY QM) is constructed and the various possibilities for partial supersymmetry breaking are discussed. It is shown that quantum mechanical models with one quarter, one half and…
A parametrization of the Hamiltonian of the generalized Witten model of the SUSY QM by a single arbitrary function in d=1 has been obtained for an arbitrary number of the supersymmetries N. Possible applications of this formalism have been…
We study an intensity-dependent quantum Rabi model that can be written in terms of SU(1,1) group elements and is related to the Buck-Sukumar model for the Bargmann parameter $k=1/2$. The spectrum seems to present avoiding crossings for all…
If collider experiments demonstrate that the Minimal Supersymmetric Standard Model (MSSM) is a good description of nature at the weak scale, the experimental priority will be the precise determination of superpartner masses. These masses…
In these introductory lectures, we review the theoretical tools used in constructing supersymmetric field theories and their application to physical models. We first introduce the technology of two-component spinors, which is convenient for…