Two-dimensional Bose gas at low density

Abstract

We propose a new method to describe the interacting bose gas at zero temperature. We use the decomposition of the logarithm of the wave function into the irreducible $n$-point functions. We argue that in the low density limit this expansion corresponds to the expansion of the ground-state energy in powers of the small parameter. For three-dimensional system the correction to the ground-state energy in density is reproduced. For two-dimensional dilute bose gas the ground- state energy in the leading order in the parameter $|\ln\a^2\rho|^{-1}$ where $\a$ is a scattering length is obtained.