New symmetry in many-body effective Hamiltonians: An example of rotating nuclei

A general class of many-body Hamiltonians containing one- and two-body interactions that obey at least one dichotomic symmetry are considered. A rich subset in that class with several important physical applications (such as, e.g., in nuclear superfluidity and/or particle number nonconserving Hamiltonians) are studied from a unitary-group structure point of view. Those Hamiltonians are shown to obey a symmetry called further on scrP symmetry. A corresponding Casimir operator is constructed together with its eigenvalues and the implied classification of the spectra is illustrated on a nuclear-physics example with a single-j shell Hamiltonian. The most general form of a scrP-symmetric Hamiltonian is discussed