Incompleteness of Representation Theory: Hidden symmetries and Quantum Non-Integrability

Abstract

Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of these hidden symmetries depends upon the realization of the Hamiltonian.

Comments: 4 pages, Revtex, Phys. Rev. Lett. , July 27 (1997), in press