Scattering amplitudes from finite-volume spectral functions

Understand

A novel proposal is outlined to determine scattering amplitudes from finite-volume spectral functions.

• The method requires extracting smeared spectral functions from finite-volume Euclidean correlation functions, with a particular complex smearing kernel of width $\epsilon$ which implements the standard $i\epsilon$-prescription.
• In the $L \to \infty$ limit these smeared spectral functions are therefore equivalent to Minkowskian correlators with a specific time ordering to which a modified LSZ reduction formalism can be applied.
• The approach is presented for general $m \to n$ scattering amplitudes (above arbitrary inelastic thresholds) for a single-species real scalar field, although generalization to arbitrary spins and multiple coupled channels is likely straightforward.