where V ( t , x ) = e H 0 t V ( 0 , x ) e − − H 0 t evolves in Euclidean time in the interaction picture. Hence the large- E behavior of the spectral density encodes the short-time behavior of the ⟨ ⟨ V ( t , x ) V ( 0 , y ) ⟩ ⟩ vacuum correlator, where both x,y are integrated over space. The large- E scaling can be computed in explicit theories; in general it goes as