Correlation functions of the one-dimensional Bose gas in the repulsive case

The one dimensional Bose gas is considered in the repulsive case. The ground state of the system is the Dirac sea with a finite density. The correlation function of the currents is presented in the form of the series, then^th term being the contribution ofn vacuum particles. In the strong coupling limitc then^th term decreases asc^–n. In the weak coupling limitc 0 the series is also essentially simplified. The decomposition gives the uniform approximation in the distance between the currents. The arguments in favour of convergence of the series are given.