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 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.
Highlights
Quantum Field Theories play an important role in many branches of physics
In most of these applications the physical system has a finite size: scattering experiments are performed in a finite accelerator/detector, solid state systems are analyzed in laboratories, even the lattice simulations of gauge theories are performed on finite lattices etc
We develop a framework which provides direct access both to excited states’ energy levels and finite volume form factors
Summary
Quantum Field Theories play an important role in many branches of physics. On the one hand, they provide the language in which we formulate the fundamental interactions of Nature including the electro-weak and strong interactions. In case of boundstates the leading exponential volume correction is the so called μ term, which originates from a process in which the particle can virtually decay in a finite volume into its constituents This idea was used to calculate the leading μ term explicitly for the simplest non-diagonal form factor in [16]. The exact determination of the finite-volume twopoint function is hopeless in interacting theories, but developing any systematic expansion leads to a systematic expansion of both the energy levels and the form factors We analyze two such expansions in this paper: in the first, we expand the two-point function in the volume, which leads to the leading exponential corrections. In appendix C we make a perturbative expansion of the finite volume two point function in the sinh-Gordon theory and extract the leading correction to the finite volume energy and form factors confirming the results of section 4. Appendix D shows the equivalence of the finite volume regularizations of [17] with our infinite volume regularizations
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