Pseudopotentials for multiparticle interactions in the quantum Hall regime

In fractional quantum Hall physics, the Hilbert space is projected to a single Landau level and the entire Hamiltonian consists of just the projected interelectron interaction. Haldane's pseudopotential formalism has been an extremely useful tool both for understanding these interactions and for understanding the quantum Hall states that result. In the current paper, we consider the analog of this pseudopotential construction that results from general M-body interactions rather than the usual (Coulomb) two-body interaction.