Symmetry-adapted perturbation expansions using unitary transformations

A new method is devised to include the symmetry in perturbation series, in case the unperturbed hamiltonian has a lower (or different in general) symmetry than the whole problem. We define a unitary transformation such that the transformed unperturbed hamiltonian will have the same symmetry as the interacting system. This new unperturbed hamiltonian is hermitian and has indeed the same eigenvalues as the old one. Usual perturbation expansions can be thence utilized. The method is illustrated through some simple examples. The non-uniqueness of the defined unitary transformation is discussed.