Gu, XY (reprint author), CCAST, World Lab, POB 8730, Beijing 100080, Peoples R China.
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 [mu + n, nu + n, tau + n] in (D - 2n) dimensions are degenerate where mu, nu, tau, and D are given and n is an arbitrary integer if the representation [mu + n, nu + n, tau + n] exists for the SO(D - 2n) group and D - 2n greater than or equal to 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. (C) 2003 Elsevier B.V. All rights reserved.