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We develop a truncated Hamiltonian method to study nonequilibrium real timedynamics in the Schwinger model - the quantum electrodynamics in D=1+1. This isa purely continuum method that captures reliably the invariance under local andglobal gauge transformations and does not require a discretisation ofspace-time. We use it to study a phenomenon that is expected not to betractable using lattice methods: we show that the 1+1D quantum electrodynamicsadmits the dynamical horizon violation effect which was recently discovered inthe case of the sine-Gordon model. Following a quench of the model, oscillatorylong-range correlations develop, manifestly violating the horizon bound. Wefind that the oscillation frequencies of the out-of-horizon correlationscorrespond to twice the masses of the mesons of the model suggesting that theeffect is mediated through correlated meson pairs. We also report on thecluster violation in the massive version of the model, previously known in themassless Schwinger model. The results presented here reveal a novelnonequilibrium phenomenon in 1+1D quantum electrodynamics and make a first steptowards establishing that the horizon violation effect is present in gaugefield theory.

Continuum approach to real time dynamics of 1+1D gauge field theory: out of horizon correlations of the Schwinger model