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

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 $[\mu +n]$ in $(D-2n)$ dimensions are degenerate where $[\mu ]$ and $D$ are given and $n$ is an arbitrary integer if the representation $[\mu +n]$ exists for the SO($D-2n$) group and $D-2n\ge N$. 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.

8 pages, no figure, RevTex, Accepted by EuroPhys.Lett