Path Integral Representation for Composite Fermions and Bosons

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The density matrix of the 2D system of spinless electrons confined to the lowest Landau level is expressed using both basis of states parametrized by electron locations and basis of states parametrized by hole locations. In this representation, the electron-electron repulsion can be viewed as an electron-hole attraction. Electron-hole pairs stabilized by this attraction provide a new formulation for Composite Fermions which fully respects particle-hole symmetry. This representation also allows a particularly simple formulation of the composite Boson approach of generic n =p/q incompressible states: The n =p/q state corresponds to the formation of clusters made up on p electrons and q-p holes and fractionally charged excitations correspond to the breaking of such clusters.