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Physical Review Letters

Method for Solving the Massive Thirring Model

Hugh Bergknoff, H. B. Thacker

Published Jan 15, 1979• 94 citations
Publisher

Abstract

The Hamiltonian of the massive Thirring model is explicitly diagonalized by formulating a Bethe Ansatz for the eigenstates. A general method for computing the energy spectrum is presented.Received 11 August 1978DOI:https://doi.org/10.1103/PhysRevLett.42.135©1979 American Physical Society

DOI
10.1103/physrevlett.42.135

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The Hamiltonian of the massive Thirring model is explicitly diagonalized by formulating a Bethe Ansatz for the eigenstates. A general method for computing the energy spectrum is presented.Received 11 August 1978DOI:https://doi.org/10.1103/PhysRevLett.42.135©1979 American Physical Society
The Hamiltonian of the massive Thirring model is explicitly diagonalized by formulating a Bethe ansatz for the eigenstates. The physical states are described by many-body wave functions representing the vacuum as a filled Fermi-Dirac sea and particle states as excitations built upon it. The spectrum of states is determined by imposing periodic boundary conditions on the wave functions. The energies are calculated by reducing the periodic boundary conditions to linear integral equations. For fermion-antifermion bound states the Dashen-Hasslacher-Neven spectrum is obtained. It is shown that the solution to the massive Thirring model can be understood as the critical limit of Baxter's solution of the eight-vertex model.
A new method based on the SSS-matrix factorization is developed for the thermodynamics of the massive Thirring model. The method can be applied to any charge sector and coupling constant. In the zero-charge sector, the present theory reproduces all the Bethe-Ansatz-theory results in the attractive-coupling regime, and agrees with a perturbation calculation in the repulsive-coupling regime.