XXVII Workshop on Geometric Methods in Physics 29.06-05.07.2008

Edwin Langmann

Noncommutative field theories, exact solutions, and 2D correlated systems

I will discuss examples of quantum field theories on noncommutative spaces which can be solved exactly. These models have relatives which describe exactly solvable quantum many-body systems in two space dimensions and with non-trivial spatial correlations. This class of models provide interesting variational states for realistic 2D interacting fermion- and boson models which allow to generalize mean field theory so as to take into account non-trivial spatial correlations. I will discuss the relevance of these models in the context of condensed matter physics.