## Correlation functions of the one-dimensional Bose gas in the repulsive case.(English)Zbl 1062.82501

Summary: 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, the $$n$$th term being the contribution of $$n$$ vacuum particles. In the strong coupling limit $$c\to\infty$$ the $$n$$th term decreases as $$c^{-n}$$. In the weak coupling limit $$c\to 0$$ 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.

### MSC:

 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 81R12 Groups and algebras in quantum theory and relations with integrable systems 81T25 Quantum field theory on lattices
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### References:

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