  We develop a novel real-time approach to computing the entanglement between
spatial regions for Gaussian states in quantum field theory. The entanglement
entropy is characterized in terms of local correlation functions on space-like
Cauchy hypersurfaces. The framework is applied to explore an expanding light
cone geometry in the particular case of the Schwinger model for quantum
electrodynamics in 1+1 space-time dimensions. We observe that the entanglement
entropy becomes extensive in rapidity at early times and that the corresponding
local reduced density matrix is a thermal density matrix for excitations around
a coherent field with a time dependent temperature. Since the Schwinger model
successfully describes many features of multiparticle production in $e^+ e^-$
collisions, our results provide an attractive explanation in this framework for
the apparent thermal nature of multiparticle production even in the absence of
significant final state scattering.
