Related papers: Supersymmetric quantum mechanical generalized MIC-…
We extend a model of the Dirac gauginos, which originate from N=2 supersymmetry (SUSY) for the gauge sector, such that the N=2 SUSY is imposed also to the sfermion sector but only for the 3rd generation squarks and sleptons. In addition to…
A novel family of exactly solvable quantum systems on curved space is presented. The family is the quantum version of the classical Perlick family, which comprises all maximally superintegrable 3-dimensional Hamiltonian systems with…
Within a Supersymmetric Quantum Mechanics (SUSY-QM) framework, the (3+1) Dirac equation describing a Dirac material in the presence of external parallel electric and magnetic fields is solved. Considering static but non-uniform electric and…
We study, in detail, the supersymmetric quantum mechanics of charge-(1,1) monopoles in N=2 supersymmetric Yang-Mills-Higgs theory with gauge group SU(3) spontaneously broken to U(1) x U(1). We use the moduli space approximation of the…
We propose the general scheme of incorporation of the Dirac monopoles into mechanical systems on the three-dimensional conformal flat space. We found that any system (without monopoles) admitting the separation of variables in the elliptic…
A simple way to find solutions of the Painlev\'e IV equation is by identifying Hamiltonian systems with third-order differential ladder operators. Some of these systems can be obtained by applying supersymmetric quantum mechanics (SUSY QM)…
We study the super and dynamical symmetries of a fermion in a monopole background. The Hamiltonian also involves an additional spin-orbit coupling term, which is parameterized by the gyromagnetic ratio. We construct the superinvariants…
We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges…
We discuss a set of novel discrete symmetries of a free N = 2 supersymmetric (SUSY) quantum mechanical system which is the limiting case of a widely-studied interacting SUSY model of a charged particle constrained to move on a sphere in the…
The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite…
A gauge invariant mathematical formalism based on deformation quantization is outlined to model an $\mathcal{N}=2$ supersymmetric system of a spin $1/2$ charged particle placed in a nocommutative plane under the influence of a vertical…
We make a detailed study of the first and second-order SUSY partners of a one-dimensional free Hamiltonian with a singular perturbation proportional to a Dirac delta function. It is shown that the second-order transformations increase the…
We study cascade hierarchy in supersymmetric SU(5) grand unified theory. The neutrino Dirac mass matrix of the cascade form can lead to the tri-bimaximal generation mixing at the leading order in the seesaw mechanism while the down quark…
Making use of the first- and second-order algorithms of supersymmetric quantum mechanics (SUSY-QM), we construct quantum mechanical Hamiltonians whose spectra are related to the zeroes of the Riemann Zeta function $\zeta(s)$. Inspired by…
We propose an extension of {\em supersymmetric quantum mechanics} which produces a family of isospectral hamiltonians. Our procedure slightly extends the idea of intertwining operators. Several examples of the construction are given.…
The multidimensional N=4 supersymmetric quantum mechanics (SUSY QM) is constructed using the superfield approach. As a result, the component form of the classical and quantum Lagrangian and Hamiltonian is obtained. In the considered SUSY QM…
Dirac's theory of constrained Hamiltonian systems is applied to the minimal conformally invariant SU(5) grand-unified model studied at 1-loop level in a de Sitter universe. For this model, which represents a simple and interesting example…
The Coulomb branch of $N=2$ supersymmetric gauge theories in four dimensions is described in general by an integrable Hamiltonian system in the holomorphic sense. A natural construction of such systems comes from two-dimensional gauge…
A nuclear physics example of the U(6/2) supersymmetry group is considered. It is shown that this group contains a supersymmetric subgroup with a structure similar to the SUSY model of the quantum field theory (QFT). A comparison of two…
We propose a generalization of pseudospin and spin symmetries, the SU(2) symmetries of Dirac equation with scalar and vector mean-field potentials originally found independently in the 70's by Smith and Tassie, and Bell and Ruegg. As…