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