Field-theoretic approach to many-boson systems

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Abstract
It is now well established that current and density may be used as coordinates in describing a nonrelativistic many-body system. The current and density operators form a closed algebra as they obey a set of equal-time commutation relations. A particular choice of the algebra containing only the longitudinal component of the current describes a fluid in a simple way. For Bose systems, we show that there exists a special choice of this longitudinal current which is an irreducible representation of the algebra, but expressed in two different ways leading to the formulations of Bogoliubov and Zubarev (BZ) and that of Sunakawa and his coworkers (S). This demonstration proves the formal equivalence of the two formulations. The BZ formalism leads to a non-Hermitian Hamiltonian for which use of a certain mathematical technique recently proposed by us yields completely divergence-free results for Bose systems. A temperature-dependent matrix Green's-function theory is developed and the self-energy matrix calculated. From this, we also deduce the structure factor in a straightforward way. These results are applied here to compute numerically the excitation spectrum of the superfluid liquid helium using the experimental structure factor as the only input into the computation. Comparison of this with other calculations and with experiment is discussed in detail in this paper. The problem of a charged Bose gas is considered as a testing ground for all theories of Bose fluids since certain exact results are known for this system. We have applied our method using the BZ Hamiltonian to this problem and we are in complete agreement with the exact results. It thus appears that the current-algebra approach can be quite successfully applied in elucidating properties of interacting Bose systems.