Prepared for submission to JHEP Field theoretical derivation of L¨uscher’s formula and calculation of finite volume form factors aZolt´an Bajnok1,aJ´anos Balog2,a,bM´arton L´ajer3,aChao Wu4 aMTA Lend¨ulet Holographic QFT Group, Wigner Research Centre for Physics H-1525 Budapest 114, P.O.B. 49, Hungary bInstitute for Theoretical Physics, E¨otv¨os Lor´and University H-1117 Budapest P´azm´any P. s. 1/A, Hungary Abstract:We initiate a systematic method to calculate both the finite volume energy levels and form factors from the momentum space finite volume two-point function. By expanding the two point function in the volume we extracted the leading exponential volume correction both to the energy of a moving particle state and to the simplest non-diagonal form factor. The form factor corrections are given in terms of a regularized infinite volume 3-particle form factor and terms related to the L¨usher correction of the momentum quantization. We tested these results against second order Lagrangian and Hamiltonian perturbation theory in the sinh-Gordon theory and we obtained perfect agreement. ArXiv ePrint:1802.04021 1bajnok.zoltan@wigner.mta.hu 2balog.janos@wigner.mta.hu 3lajerm@caesar.elte.hu 4chao.wu@wigner.mta.hu arXiv:1802.04021v3 [hep-th] 10 Jul 2018
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