Partial dynamical symmetry

A novel type of symmetry structure, which the authors call 'partial dynamical symmetry', is discussed. A general algorithm is presented to construct Hamiltonians with such symmetry, for any semisimple group. These Hamiltonians are not invariant under that group, and various irreducible representations are mixed in their eigenstates. However, they possess a subset of eigenstates which do have good symmetry and can therefore be labelled by the irreducible representations of that group. The eigenvalues and wavefunctions of these states are given in closed form. An example of a Hamiltonian with a partial SU(3) symmetry is provided.