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arXiv · 1508.05954

An exactly solvable quantum four-body problem associated with the symmetries of an octacube

Maxim Olshanii·Steven G. Jackson
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Abstract

In this article, we show that eigenenergies and eigenstates of a system consisting of four one-dimensional hard-core particles with masses $6m$, $2m$, $m$, and $3m$ in a hard-wall box can be found exactly using Bethe Ansatz. The Ansatz is based on the exceptional affine reflection group $\tilde{F}_{4}$ associated with the symmetries and tiling properties of an octacube---a Platonic solid unique to four dimensions, with no three-dimensional analogues. We also uncover the Liouville integrability structure of our problem: the four integrals of motion in involution are identified as invariant polynomials of the finite reflection group $F_{4}$, taken as functions of the components of momenta.

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Maxim Olshanii, Steven G. Jackson. 2015-08-24. An exactly solvable quantum four-body problem associated with the symmetries of an octacube. https://arxiv.org/abs/1508.05954

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