A theoretical study of persistent currents in liquid
He4 is given, in which a system of
N interacting bosons confined to a cylindrical container is chosen as a model. It is argued that these currents are metastable and a general model-independent stability criterion valid for all temperatures is derived. In this formulation it is essential that there is a single-particle state ${\ensuremath{\phi}}_{c}$ with nonzero angular momentum
lc which is occupied by a macroscopic number [
O(N)] of particles. The stability criterion is applied to the study of two soluble models, one, an independent-particle model studied for all temperatures, the other a quasiparticle model studied for
T=0\ifmmode^\circ\else\textdegree\fi{}K. For both models persistent currents are possible at
T=0 provided that the interactions between particles are sufficiently strong and
lc does not exceed a characteristic critical value
lM. The quantity
lM is calculated for different choices of single-particle functions, and in particular for the solutions of a Hartree equation, which is relevant to a description of line vortices with quantized circulation. The density ${\ensuremath{\rho}}_{c}(T)$ of particles macroscopically occupying ${\ensuremath{\phi}}_{c}$ at a temperature
T, as well as the critical temperature
T∗ above which no persistent currents are possible, are calculated for the independent-particle model.
The present paper attempts to give independent descriptions of the collective degrees of freedom of nuclei such as the monopole and quadrupole ones in order to avoid the seniority mixing problem. This is done by the operatorized Bogoliubov transformation (OBT) which separates the degree of freedom from the rest described by the seniority particle operator which is not coupling to the pairs, and in terms of which the independent pair is composed. The OBT is derived in such a way that it can be generalized easily to include a new kind of “seniority particle operator” neither coupling to the nor to the pairs. In terms of this new particle operator the independent pair or the independent odd particle in odd nuclei is constructed.