In two dimensional systems in a strong magnetic field, electrons can be transformed into composite Fermions (CF) by attaching to each a fictitious flux tube (carrying flux (Phi)) and fictitious charge q, where the product q(sup (Phi)) is a multiple of 2 (Pi). In the mean field approximation, this transformation converts a fractionally filled electron Landau level into an integrally filled CF Landau level. This integrally filled CF Landau level corresponds to the ground state of a Laughlin incompressible fluid. Excited states are described by the n(sub QE) and n(sub QH), the numbers of quasielectron and quasihole CF excitations. For N electrons on the surface of a sphere the energy and angular momentum of a quasihole (or quasielectron) are (var epsilon)(sub QH) and l(sub QH)=1/2(N+n(sub QH)-n(sub QE)-1) (or (var epsilon)(sub QE) and l(sub QE)=l(sub QH)+1). The lowest energy sector of the energy spectrum contains the minimum number of CF excitations consistent with the value of N and the degeneracy of the lowest Landau level, 2S+1. The first excited sector contains one additional QE-QH pair. The total angular momentum L is obtained by adding the angular momenta of QE excitations and QH excitations treated as distinguished sets of Fermions. In the absence of CF interactions, all states containing n(sub QE) quasielectrons and n(sub QH) quasiholes are degenerate. The interaction between CF excitations partially removes this degeneracy. The interactions between CF excitations can be determined by comparing exact numerical results for N electrons with the CF picture. This amounts to constructing a Fermi liquid theory of CF excitations, and should allow the study of low lying excitations of systems with much larger values of N than can be treated numerically.
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