On a question of H. A. Schwarz

This paper is a contribution to the study of tetrahedra with rational side lengths and rational volume. The problem can be formulated as a study of a hyperelliptic variety attached to the Cayley-Menger determinant. The problem posed by Schwarz was as to whether this variety is rational over the rationals. In a thesis that was never published Otto Schulz proved in 1912 that the variety was rational over $\mathbb Q(\sqrt{-1})$. This does not seem to have appeared eleswhere nor, apparently, has the question been studied since then. In this paper we take up an idea of Kurt Heegner to reprove the theorem using the theory of Weddle surfaces. Although this does not lead to a final answer to Schwarz question it seems likely that it is negative.Comment: The mathematics described here was presented and discussed at the conference "Thermodynamics Formalism- Applications to Geometry, Number Theory and Stochastics" (8th-12th July, 2019) at the Mittag-Leffler Institute, Djursholm This is the revised version following the referee's repor

The Muon Collider as a H/AH/A factory

We show that a muon collider is ideally suited for the study of heavy H/A scalars, cousins of the Higgs boson found in two-Higgs doublet models and required in supersymmetric models. The key aspects of H/A are: (1) they are narrow, yet have a width-to-mass ratio far larger than the expected muon collider beam-energy resolution, and (2) the larger muon Yukawa allows efficient s-channel production. We study in detail a representative Natural Supersymmetry model which has a 1.5 Tev H/A with $m_H$- $m_A$ = 10 Gev. The large event rates at resonant peak allow the determination of the individual H and A resonance parameters (including CP) and the decays into electroweakinos provides a wealth of information unavailable to any other present or planned collider.Comment: 7 pages, 2 figure

Study of e+e- -> H+H- at a 800 GeV Linear Collider

The production and decay of heavy charged Higgs bosons at a 800 GeV e+e- linear collider have been studied. The analysis of the H+H- -> tb tb, expected to be dominant in the MSSM, and H+H- -> W+h0 W-h0 decay modes leading to the same final state consisting of two W bosons and four b quarks, provides with a determination of the boson mass to 1 GeV and of the production cross section with 10% accuracy for 500 fb-1 of data.Comment: 4 pages, 1 figure, to appear in the Proceedings of the 5th Linear Collider Workshop Fermilab, October 200

A separable non-remainder of H

We prove that there is a compact separable continuum that (consistently) is not a remainder of the real line.Comment: Rewrite after referee's comment

A new tunneling path for reactions such as H+H_2→H_2+H

The standard tunneling path in transition state theory for reactions such as H+H_2→H_2+H has been the so‐called reaction path, namely the path of steepest ascent to the saddle point. This path is now known to give numerical results for the reaction probability which are in disagreement with the exact quantum mechanical ones by an order of magnitude at low tunneling energies. A new tunneling path corresponding to a line of vibrational endpoints is proposed. It is much shorter and is shown to give results in agreement with the quantum ones to within about a factor of two. A semiclassical basis for choosing this new path is given