Hamiltonian formulation of the W1+infinity minimal models

The W1+infinity minimal models are conformal field theories which can descr ibe the edge excitations of the hierarchical plateaus in the quantum Hall e ffect. In this paper, these models are described in very explicit terms by using a bosonic Fock space with constraints, or, equivalently, with a non-t rivial Hamiltonian. The Fock space is that of the multi-component abelian c onformal theories, which provide another possible description of the hierar chical plateaus; in this space, the minimal models are shown to correspond to the sub-set of states which satisfy the constraints. This reduction of d egrees of freedom can also be implemented by adding a relevant interaction to the Hamiltonian, leading to a renormalization-group flow between the two theories. Next, a physical interpretation of the constraints is obtained b y representing the quantum incompressible Hall fluids as generalized Fermi seas. Finally, the non-abelian statistics of the quasi-particles in the W1infinity minimal models is described by computing their correlation functio ns in the Coulomb gas approach. (C) 1999 Elsevier Science B.V.