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Field theoretical derivation of L\"uscher's formula and calculation of finite volume form factors
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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.
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Finite volume corrections of non-diagonal form factors
The mu-term corrections from bound-state quantization are reproduced exactly as residues of the F-term integral for elementary non-diagonal form factors, confirming the connection between the two formalisms.
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