Showing papers on "Superpotential published in 1985"

Supersymmetric quantum mechanics of one-dimensional systems

Abstract: It is shown that every one-dimensional quantum mechanical Hamiltonian H1 can have a partner H2 such that H1 and H2 taken together may be viewed as the components of a supersymmetric Hamiltonian. The term 'supersymmetric Hamiltonian' is taken to mean a Hamiltonian defined in terms of charges that obey the same algebra as that of the generators of supersymmetry in field theory. The consequences of this symmetry for the spectra of H1 and H2 are explored. It is shown how the supersymmetric pairing may be utilised to eliminate the ground state of H1, or add a state below the ground state of H1 or maintain the spectrum of H1. It is also explicitly demonstrated that the supersymmetric pairing may be used to generate a class of anharmonic potentials with exactly specified spectra. The complete spectrum of an anharmonic potential so generated consists of all the eigenstates of the simple harmonic oscillator and, in addition, a ground state at a specified energy E which lies arbitrarily below the E=1/2 ground state of the harmonic oscillator.

Supersymmetric quantum mechanics and large-N expansions.

Abstract: Supersymmetric quantum mechanics is formulated for spherically symmetric potentials in N spatial dimensions. It is seen that the supersymmetric partner potential of a given potential can be effectively treated as being in N+2 dimensions. This fact is exploited in calculations using the shifted 1/N expansion. Also, the violation of the no-degeneracy theorem in one dimension by the Coulomb potential is seen as a consequence of this result.

Supersymmetric quantum mechanical models with continuous spectrum and the Witten index

Abstract: The authors discuss supersymmetric regularisations of soluble supersymmetric quantum mechanical models with continuous parts to the energy spectra. Results include a demonstration that the Witten index changes discontinuously from zero to one upon removal of the regularisation.

Supergravitational Radiative Corrections to the Gauge Hierarchy

Abstract: We compute one-loop radiative corrections, including contributions from virtual gravitons and gravitinos, to the scalar potential in $N=1$ supergravity with an arbitrary superpotential. We show that, in a large class of locally supersymmetric grand unified theories, these corrections do not upset the tree-level gauge hierarchy.

Study of a three-dimensional quantum-mechanical supersymmetric model with nucleon-nucleon-type interaction

Abstract: We study a three-dimensional quantum-mechanical supersymmetric model, characterized by a potential with central, spin-spin, and tensor terms, which describes the interaction of two spin-(1/2) particles, each one endowed with an extra internal charge. A particular realization of this model reproduces the long-range behavior of the nucleon-nucleon interaction for each isospin channel. We discuss the complete set of commuting operators for the system paying special attention to the fermionic number operator which is peculiar to supersymmetric systems. We also consider the effect of the supersymmetry generators upon such a set. In terms of the radial functions, we explicitly write down the full set of first-order coupled differential equations which define any N = 1 supersymmetric system. They reflect the fact that the supersymmetry generators act as raising and lowering operators among the different channels of the interaction. Using this information we analyze the scattering regime of the model and obtain the constraints that supersymmetry imposes upon the mixing angles and phase shifts of the system. These predictions are illustrated by independently solving the example of a spherical-well superpotential. Finally we discuss the problem of spontaneous supersymmetry breaking in our model.

Supersymmetric generalization of Todorov's equation

Abstract: The author considers a supersymmetric generalization of the quasipotential equation in the Markov-Yukawa gauge. Imposition of the supersymmetric Markov-Yukawa condition on the twoparticle Bethe-Salpeter amplitude yields conditions that give the transition to a one-time wave function. For this wave function, a supersymmetric three-dimensional equation is written down. The Born term of the quasipotential is found for a self-interacting chiral superfield, and also for interaction with a massless chiral superfield.

Hemivariational Inequalities. Existence and Approximation Results

Abstract: The theory of variational inequalities is closely connected to the notion of superpotential introduced by Moreau1 for convex generally non-differentiable and nonfinite energy functionals. If Φ is such a functional, a superpotential relation (material law or boundary condition) in the sense of Moreau has the form $$f \in \partial \Phi \left( u \right)$$ (1.1) where f and u are a “force” and a “flux” respectively in the terminology of Onsager’s theory and ∂ denotes the subdifferential2, which is a monotone multivalued operator. Such a law allows the derivation of variational inequalities3, 4 which are expressions of the principle of virtual or complementary virtual work (or power) in static problems and of d’ Alembert’s principle in dynamic problems.