### Abstract

We propose thermodynamic Bethe ansatz (TBA) integral equations for multiparticle soliton (fermion) states in the sine-Gordon (massive Thirring) model. This is based on T-system and Y-system equations, which follow from the Bethe ansatz solution in the light-cone lattice formulation of the model. Even and odd charge sectors are treated on an equal footing, corresponding to periodic and twisted boundary conditions, respectively. The analytic properties of the Y-system functions are conjectured on the basis of the large volume solution of the system, which we find explicitly. A simple relation between the TBA Y-functions and the counting function variable of the alternative non-linear integral equation (Destri-deVega equation) description of the model is given. At the special value β^{2} = 6π of the sine-Gordon coupling, exact expressions for energy and momentum eigenvalues of one-particle states are found.

Original language | English |
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Pages (from-to) | 1903-1925 |

Number of pages | 23 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 37 |

Issue number | 5 |

DOIs | |

Publication status | Published - Feb 6 2004 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)