  I present a novel class of exactly solvable quantum field theories. They
describe non-relativistic fermions on even dimensional flat space, coupled to a
constant external magnetic field and a four point interaction defined with the
Groenewold-Moyal star product. Using Hamiltonian quantization and a suitable
regularization, I show that these models have a dynamical symmetry
corresponding to $\gl_\infty\oplus \gl_\infty$ at the special points where the
magnetic field $B$ is related to the matrix $\theta$ defining the star product
as $B\theta=\pm I$. I construct all eigenvalues and eigenstates of the
many-body Hamiltonian at these special points. I argue that this solution
cannot be obtained by any mean-field theory, i.e. the models describe
correlated fermions. I also mention other possible interpretations of these
models in solid state physics.
