The Thirring–Wess model or Vector Meson model is an exactly solvable quantum field theory, describing the interaction of a Dirac field with a vector field in dimension two. Definition The Lagrangian density is made of three terms: the free vector field is described by for and the boson mass must be strictly positive; the free fermion field is described by where the fermion mass can be positive or zero. And the interaction term is Although not required to define the massive vector field, there can be also a gauge-fixing term for There is a remarkable difference between the case and the case : the latter requires a field renormalization to absorb divergences of the two point correlation. History This model was introduced by Thirring and Wess as a version of the Schwinger model with a vector mass term in the Lagrangian . When the fermion is massless (), the model is exactly solvable. One solution was found, for , by Thirring and Wess using a method introduced by Johnson for the Thirring model; and, for , two different solutions were given by Brown and Sommerfield. Subsequently Hagen showed (for , but it turns out to be true for ) that there is a one parameter family of solutions. References External links Quantum field theory Exactly solvable models