RT info:eu-repo/semantics/article
T1 The general Racah algebra as the symmetry algebra of generic systems on pseudo-spheres
A1 Kuru, Şengül
A1 Marquette, I
A1 Negro Vadillo, Francisco Javier
AB We characterize the symmetry algebra of the generic superintegrable systemon a pseudo-sphere corresponding to the homogeneous space SO(p, q + 1)/SO(p, q) where p+ q = N,N ∈N. These symmetries occur both in quantumas well as in classical systems in various contexts, so they are quite important inphysics.We show that this algebra is independent of the signature (p, q + 1) ofthe metric and that it is the same as the Racah algebraR(N + 1). The spectrumobtained from R(N + 1) via the Daskaloyannis method depends on undeterminedsigns that can be associated to the signatures. Two examples are workedout explicitly for the cases SO(2, 1)/SO(2) and SO(3)/SO(2) where it is shownthat their spectrum obtained by means of separation of variables coincide withparticular choices of the signs, corresponding to the specific signatures, of thespectrum for the symmetry algebra R(3).
PB IOP publishing
SN 1751-8113
YR 2020
FD 2020
LK https://uvadoc.uva.es/handle/10324/81437
UL https://uvadoc.uva.es/handle/10324/81437
LA spa
NO J. Phys. A: Math. Theor. 53 (2020) 405203 (10pp)
DS UVaDOC
RD 06-abr-2026