It is shown that the coherent-state representation of a many-boson wave function may be identified with the order-parameter function conventionally used to describe a superfluid. The statistical mechanics of the many-boson system is reformulated in terms of the coherent states, and a theory of the Ginzburg-Landau form is recovered in an obvious approximation. The formalism is particularly useful for describing metastable states of finite superflow and the fluctuations which may cause spontaneous decay of such states.
A theory is formulated for the ground state of a degenerate Bose fluid in thermal equilibrium. The fluctuations in the condensate are treated in terms of the fluctuation operators C = a 0 -α, and thir conjugate, α 0 being the annihilation operator for the zero momentum state and the order parameter α the quasiaverage of α 0 . The superfluid ground state is viewed as energy lowering by coherent excitations. The coherent state is defined in terms of the normal modes in the superfluid phase. The superfluid ground state is not the ground state of the type studied by Glassgold and Sauermann.
The coherent-state formalism is used to develop a theory of fluctuations and irreversible processes in a superfluid Bose system. Equations of motion for the density matrix are derived both for the case of an isolated system and for the system in interaction with a heat bath. The formalism allows one to go easily to the classical limit and thus to obtain equations for the probability distribution of the superfluid order parameter. The results are in a form suitable for the calculation of the decay of superflow near the $\ensuremath{\lambda}$ point and other similar phenomena.