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In this paper we give a new derivation of the generalized Luscher F-termformula from a summation over quadratic fluctuations around a given soliton.The result is very general providing that S-matrix is diagonal and is valid forarbitrary dispersion relation. We then apply this formalism to compute theleading finite size corrections to the giant magnon dispersion relation comingfrom quantum fluctuations.

A new derivation of Luscher F-term and fluctuations around the giant magnon