Collective excitation gap in the fractional quantum Hall effect.

We present a theory of the collective excitation spectrum in a fractional quantum Hall effect regime, in analogy with Feynman's theory for helium. The spectrum is in excellent quantitative agreement with the numerical results of Haldane. Within this approximation we prove that a finite gap is generic to any liquid state in the extreme quantum limit. Gapless excitations can arise only as Goldstone modes for ground states with broken translation symmetry.