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Interdimensional degeneracies for a quantum $N$-body system in $D$ dimensions

Xiao-Yan Gu·Zhong-Qi Ma·Jian-Qiang Sun
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Abstract

Complete spectrum of exact interdimensional degeneracies for a quantum $N$-body system in $D$-dimensions is presented by the method of generalized spherical harmonic polynomials. In an $N$-body system all the states with angular momentum $[μ+n]$ in $(D-2n)$ dimensions are degenerate where $[μ]$ and $D$ are given and $n$ is an arbitrary integer if the representation $[μ+n]$ exists for the SO($D-2n$) group and $D-2n\geq N$. There is an exceptional interdimensional degeneracy for an $N$-body system between the state with zero angular momentum in $D=N-1$ dimensions and the state with zero angular momentum in $D=N+1$ dimensions.

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Xiao-Yan Gu, Zhong-Qi Ma, Jian-Qiang Sun. 2003-09-23. Interdimensional degeneracies for a quantum $N$-body system in $D$ dimensions. https://doi.org/10.1209/epl%2Fi2003-00617-9

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