INTEGRABLE FIELD THEORIES

Recent developments on integrable field theories and statistical models in two dimensions are reviewed.

The best way to investigate the continuum limit of lattice models is through the light-cone approach. This method allows to find the underlying quantum field theory for any integrable lattice model in its gapless regime. The relativistic spectrum and S-matrix follows straightforwardly in this way through the Bethe Ansatz. We show here how to derive the infinite number of local commuting and non-local and non-commuting conserved charges in integrable QFT, taking the massive Thirring model (sine-Gordon) as an example. They are generated by quantum monodromy operators and provide a representation of q–deformed affine Lie algebras . Therefore, these models enjoy infinite dimensional non-abelian symmetries.

A new lattice local formulation of integrable field models is presented and applied to the massive Thirring model (sine-Gordon) as an example.

Finally, the new thermodynamic Bethe Ansatz (DDV equations) allowing an unified treatment of finite size and finite temperature integrable models is reviewed.