Related papers: Supersymmetrical Separation of Variables for Scarf…
The $\cal PT$-symmetric complexified Scarf II potential $V(x)= - V_1 \sech^{2}x + {\rm i} V_2 \sech x \tanh x$, $V_1>0$ , $V_{2}\neq 0$ is revisited to study the interplay among its coupling parameters. The existence of an isolated real and…
A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin 0 and 1/2, is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components…
Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action fuctional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The…
We obtain the one- and two-loop renormalization group equations for soft SUSY breaking scalar interactions in general, semi-simple SUSY gauge model, by using the supergraph method. We find that the method simplifies the calculation…
In this paper we apply our new separation of variables approach to completely characterize the transfer matrix spectrum for quantum integrable lattice models associated to fundamental evaluation representations of $\mathcal{U}_{q}…
We construct a pseudoclassical particle model associated to the twisted N=2 SUSY algebra in four dimensions. The particle model has four kappa symmetries. Three of them can be used to reduce the model to the vector supersymmetry particle…
In paper approach of double complex SUSY-transformations with not coincident complex energies of transformation is developed, allowing to deform given real potential $V_{1}$ with obtaining exact solutions. The explicit solutions of the…
Supersymmetric (SUSY) models and dynamical breaking of symmetries have been used to explain hierarchies of mass scales. We find that a chiral representation, $\overline{\bf 10}\, \oplus\, \overline{\bf 5}\, \oplus\, 2\cdot{\bf 5}$ in SUSY…
We study the grand unification model flipped $SU(5)$ with additional vector-like particle multiplets, or ${\cal F}$-$SU(5)$ for short, in the framework of General No-Scale Supergravity. In our analysis we allow the supersymmetry (SUSY)…
We initiate a research program for the systematic investigation of quantum superintegrable systems involving the interaction of two non-relativistic particles with spin $1/2$ moving in the three-dimensional Euclidean space. In this paper,…
The relation between a N = 2 nonlinear supersymmetric (SUSY) model and a linear SUSY (free) theory for $N = 2$ vector supermultiplet accompanying the spontaneous SUSY breaking is systematically worked out in two-dimensional superfield…
The quantization of the most general Bianchi Type II geometry -with all six scale factors, as well as the lapse function and the shift vector, present- is considered. In an earlier work, a first reduction of the initial 6-dimensional…
In this paper, we search the factorizations of the shape invariant Hamiltonians with Scarf II potential. We find two classes; one of them is the standard real factorization which leads us to a real hierarchy of potentials and their energy…
The class of relativistic spin particle models reveals the `quantization' of parameters already at the classical level. The special parameter values emerge if one requires the maximality of classical global continuous symmetries. The same…
Separation of variables (SoV) is an extremely efficient and elegant technique for analysing physical systems but its application to integrable spin chains was limited until recently to the simplest su(2) cases. In this paper we continue…
We generalize the formalism and the techniques of the supersymmetric (susy) quantum mechanics to the cases where the superpotential is generated/defined by higher excited eigenstates. The generalization is technically almost straightforward…
Classical integrable Hamiltonian systems generated by elements of the Poisson commuting ring of spectral invariants on rational coadjoint orbits of the loop algebra $\wt{\gr{gl}}^{+*}(2,{\bf R})$ are integrated by separation of variables in…
We propose a possible new way to resolve the long standing problem of strong supersymmetry breaking coexisting with a small cosmological constant. We consider a scalar component of a minimally coupled N=1 supermultiplet in a general…
We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or…
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…