Field theoretical derivation of Lüscher’s formula and calculation of finite volume form factors. (English) Zbl 1395.81169
Summary: 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 Lüsher 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.
MSC:
| 81T16 | Nonperturbative methods of renormalization applied to problems in quantum field theory |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
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