Comment on "Summing One-Loop Graphs at Multi-Particle Threshold"

The propagator of a virtual $\phi$-field with emission of $n$ on-mass-shell particles all being exactly at rest is calculated at the tree-level in $\lambda \phi^4$ theory by directly solving recursion equations for the sum of Feynman graphs. It is shown that the generating function for these propagators is equivalent to a Fourier transform of the recently found Green's function within the background-field technique for summing graphs at threshold suggested by Lowell Brown. Also the derivation of the result that the tree-level on-mass-shell scattering amplitudes of the processes $2 \to n$ are exactly vanishing at threshold for $n > 4$ is thus given in the more conventional Feynman diagram technique.Comment: 7 pages, LaTeX, TPI-MINN-92/46-

Selfadjoint and mm sectorial extensions of Sturm-Liouville operators

The self-adjoint and $m$-sectorial extensions of coercive Sturm-Liouville operators are characterised, under minimal smoothness conditions on the coefficients of the differential expression.Comment: accepted by IEOT, in IEOT 201

Nuclear Structure Aspects of Neutrinoless Double Beta Decay

We decompose the neutrinoless double-beta decay matrix elements into sums of products over the intermediate nucleus with two less nucleons. We find that the sum is dominated by the J^pi=0^+ ground state of this intermediate nucleus for both the light and heavy neutrino decay processes. This provides a new theoretical tool for comparing and improving nuclear structure models. It also provides the connection to two-nucleon transfer experiments.Comment: 5 pages, 6 figure