Super-Grassmannian and large N limit of quantum field theory with bosons and fermions

We study a large N_c limit of a two-dimensional Yang–Mills theory coupled to bosons and fermions in the fundamental representation. Extending an approach due to Rajeev we show that the limiting theory can be described as a classical Hamiltonian system whose phase space is an infinite-dimensional super-Grassmannian. The linear approximation to the equations of motion and the constraint yields the ’t Hooft equations for the mesonic spectrum. Two other approximation schemes to the exact equations are discussed.