3 research outputs found
Extended Supersymmetries and the Dirac Operator
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
that exist and restrictions on the geometry of the underlying spaces as well as
the admissible gauge field configurations. From the superalgebra with two or
more real supercharges we infer the existence of integrability conditions and
obtain a corresponding superpotential. This potential can be used to deform the
supercharges and to determine zero modes of the Dirac operator. The general
results are applied to the Kahler spaces CP^n.Comment: 22 pages, no figure
From the Dirac Operator to Wess-Zumino Models on Spatial Lattices
We investigate two-dimensional Wess-Zumino models in the continuum and on
spatial lattices in detail. We show that a non-antisymmetric lattice derivative
not only excludes chiral fermions but in addition introduces supersymmetry
breaking lattice artifacts. We study the nonlocal and antisymmetric SLAC
derivative which allows for chiral fermions without doublers and minimizes
those artifacts. The supercharges of the lattice Wess-Zumino models are
obtained by dimensional reduction of Dirac operators in high-dimensional
spaces. The normalizable zero modes of the models with N=1 and N=2
supersymmetry are counted and constructed in the weak- and strong-coupling
limits. Together with known methods from operator theory this gives us complete
control of the zero mode sector of these theories for arbitrary coupling.Comment: 39 pages, 3 figure
Algebraic Solution of the Supersymmetric Hydrogen Atom in d Dimensions
In this paper the N=2 supersymmetric extension of the Schroedinger
Hamiltonian with 1/r-potential in arbitrary space-dimensions is constructed.
The supersymmetric hydrogen atom admits a conserved Laplace-Runge-Lenz vector
which extends the rotational symmetry SO(d) to a hidden SO(d+1) symmetry. This
symmetry of the system is used to determine the discrete eigenvalues with their
degeneracies and the corresponding bound state wave functions.Comment: 36 pages, 6 figure