Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-05-28
Nucl.Phys. B654 (2003) 404-426
Physics
High Energy Physics
High Energy Physics - Theory
23 pages, LaTex
Scientific paper
10.1016/S0550-3213(03)00006-3
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.
Langmann Edwin
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