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

Korepin, V. E.

Commun. Math. Phys. 94, No. 1, 93-113 (1984).

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

References:

[1]	Izergin, A. G., Korepin, V. E.: The quantum inverse scattering method approach to the correlation functions. Commun. Math. Phys.93, ? (1984) · Zbl 0538.60097
[2]	Faddeev, L. D.: Quantum completely integrable models of field theory. Sov. Sci. Rev. Math. Phys.C1, 107?160 (1981) · Zbl 1063.81643
[3]	Faddeev, L. D., Sklyanin, E. K.: Quantum mechanical approach to the completely integrable models of field theory. Dokl. Akad. Nauk SSSR243, 1430?1433 (1978)
[4]	Sklyanin, E. K.: The inverse scattering method and the quantum nonlinear Schrödinger equation. Dokl. Akad. Nauk SSSR244, 1337?1341 (1978) · Zbl 0426.47006
[5]	Lieb, E. H.: Exact Analysis of an Interacting Bose Gas I. The General Solution and the Ground State. Phys. Rev.130, 1605?1616 (1963) · Zbl 0138.23001 · doi:10.1103/PhysRev.130.1605
[6]	Lieb, E. H.: Exact Analysis of an Interacting Bose Gas II. The Excitation Spectrum. Phys. Rev.130, 1616?1624 (1963) · Zbl 0138.23002 · doi:10.1103/PhysRev.130.1616
[7]	Yang, C. N., Yang, C. P.: Thermodynamics of a One-Dimensional System of Bosons with Repulsive Delta-Function Interaction. Journ. Math. Phys.10, 1115?1122 (1969) · Zbl 0987.82503 · doi:10.1063/1.1664947
[8]	Korepin, V. E.: A Direct calculation of theS-matrix of the Massive Thirring Model. Teor. Mat. Phys.41, 169?189 (1979)
[9]	Korepin, V. E., Calculation of Norms of Bethe Wave Functions. Commun. Math. Phys.86, 391?418 (1982) · Zbl 0531.60096 · doi:10.1007/BF01212176
[10]	Destri, C., Lowenstein, J. H.: Normalization of Bethe-Ansatz States in the Chiral-Invariant Gross-Neveu Model. Preprint New-York University, NYU/TR6/82, (1?19) (1982)
[11]	Lenard, A.: Momentum Distribution in the Ground State of the One-Dimensional System of Impenetrable Bosons. J. Math. Phys.5, 930?943 (1964) · doi:10.1063/1.1704196
[12]	Lenard, A.: One-Dimensional Impenetrable Boson in Thermal Equilibrium. J. Math. Phys.7, 1268?1272 (1966) · doi:10.1063/1.1705029
[13]	Jimbo, M., Miwa, T., Mori, Y., Sato, M.: Density Matrix of an Impenetrable Gas and the Fifth Painleve Transcendent. PhysicaD1, 80?158 (1980) · Zbl 1194.82007
[14]	Creamer, O. B., Thacker, H. B., Wilkinson, D.: Some Exact Results for the Two Point Function of an Integrable Quantum Field Theory. Phys. Rev.D21, 1523?1535 (1980)
[15]	Thacker, H. B.: The Quantum Inverse Method and Green’s Functions for Completely Integrable Field Theories. Preprint. Fermilab-Conf-81/47-THY (1981)
[16]	Popov, V. N.: Longwave Asymptotics of the Manyparticle Green Functions for the One-Dimensional Bose Gas. Pisma ZETPh31, 560?563 (1980)
[17]	Karowski, M.: The Bootstrap Program for 1+1 Dimensional Field Theoretic Models With Soliton Behaviour. In: Field Theoretical Methods in Particle Physics. Ruhl, W. (ed.). New York: Plenum Publishing Corporation 1980 · Zbl 1251.81064
[18]	Korepin, V. E.: Analysis of the bilinear relation of the six vertex model. Doklady AN SSSR265, 1361?1364 (1982)