Thirring–Wess model
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 that there is a one parameter family of solutions.