Gauge field theories are used to model the interactions of elementary
particles. Their formulation relies on gauge and space-time symmetries.
Integrable quantum systems are based on larger symmetry
algebras as compared to the finitely generated ones appearing in the
construction of gauge field theories.
Yangian algebras provide a particular extension of Lie algebras.
Representations of such extended algebras and of their deformations appear in integrable quantum systems. Traditional examples of physical applications are Heisenberg spin chains, integrable two-dimensional lattice and one-dimensional scattering models.
Last two decades the gauge field theories appeared as a new range of
applications, in particular
the Regge and Bjorken asymptotics of high-energy scattering, the
composite operator renormalization, the computation of scattering amplitudes and Wilson loop correlators.
Methods originally developed in view of applications like spin chains
have been adapted and developed for these new applications.