Interdimensional degeneracies in a quantum isolated four-body system

Complete spectrum of exact interdimensional degeneracies for a quantum isolated four-body system in D dimensions is presented and proved by the method of generalized spherical harmonic polynomials. A quantum isolatd system must be invariant in a global translation and a global rotation. In a quantum isolated four-body system all the states with angular momentum [μ+n,ν+n,τ+n] in (D-2n) dimensions are degenerate where μ, ν, τ, and D are given and n is an arbitrary integer if the representation [μ+n,ν+n,τ+n] exists for the SO(D-2n) group and D-2n≥4. There is an exceptional interdimensional degeneracy for a four-body system between the state with zero angular momentum in D=3 dimensions and the state with zero angular momentum in D=5 dimensions