Wiese\
    \
    Institute for Theoretical Physics, Bern University\
    Sidlerstrasse 5, CH-3012 Bern, Switzerland\
    \
title: Discrete Accidental Symmetry for a Particle in a Constant Magnetic Field on a Torus
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Introduction
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The fact that for some physical systems all bound classical orbits are closed leads to accidental degeneracies in the discrete energy spectrum of the corresponding quantum systems. Accidental symmetries are familiar from a particle moving in a $1/r$ or $r^2$ potential. In $d$ spatial dimensions the system then has an $SO(d)$ rotational symmetry. In case of the $1/r$ potential, this symmetry is dynamically enhanced to an accidental $SO(d+1)$ symmetry, and for the $r^2$ harmonic oscillator potential it is enhanced to $SU(d)$. The accidental symmetries give rise to additional degeneracies in the discrete energy spectrum of the corresponding quantum systems, beyond the degeneracies one would expect based on rotation invariance alone [@Foc35; @Bar36]. The components of the Runge-Lenz vector [@Len24] are the generators of the accidental symmetry algebras. The subject of accidental symmetry has been reviewed, for example, by McIntosh [@McI71]. Recently, we have further investigated the phenomenon of accidental symmetries, by studying a particle confined to the surface of a cone and bound to its tip by a 