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We build the constraint that all electrons are in the lowest Landau levelinto the Chern-Simons field theory approach for the fractional quantum Hallsystem. We show that the constraint can be transmitted from one hierarchicalstate to the next. As a result, we derive in generic the equations of thefractionally charged vortices ( quasi-particles ) for arbitrary hierarchyfilling. For a finite system, we show that the action for each hierarchicalstate can be divided into two parts: the surface part provides the action forthe edge excitations while the remaining bulk part is exactly the action forthe next hierarchical states. In particular, we not only show that the surfaceaction for the edge excitations would be decoupled from the bulk at eachhierarchy filling, but also derive the explicit expressions analytically forthe drift velocities of the hierarchical edge excitations.Comment: AS-ITP-93-

Constraint for the lowest Landau level and the Chern-Simons field-theory approach for the fractional quantum Hall effect: Infinite and finite systems