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The Dynamical Algebra of the Hydrogen Atom as a Twisted Loop Algebra

C. Daboul·J. Daboul·P. Slodowy
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Abstract

We show that the dynamical symmetry of the hydrogen atom leads in a natural way to an infinite-dimensional algebra, which we identify as the positive subalgebras of twisted Kac-Moody algebras of $ so(4)$. We also generalize our results to the $N$-dimensional hydrogen atom. For odd $N$, we identify the dynamical algebra with the positive part of the twisted algebras $\hat {so}(N+1)^τ$. However, for even $N$ this algebra corresponds to a parabolic subalgebra of the untwisted loop algebra $\hat{so}(N+1)$.

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C. Daboul, J. Daboul, P. Slodowy. 1994-08-14. The Dynamical Algebra of the Hydrogen Atom as a Twisted Loop Algebra. https://arxiv.org/abs/hep-th/9408080

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