Schwinger effect in arbitrary electric fields and full backreaction in 1+1D QED using bosonization

Electron-positron pairs are created in the presence of a classical background electric field through the Schwinger effect, causing discharge of the field over time. In this talk, we demonstrate how bosonization–a map from a fermion theory to a corresponding boson theory– can be used to study the 1+1D Schwinger effect. By restricting to the strong field limit where the fermion mass is much smaller compared to the background field, we analyze the Schwinger effect as an interacting boson theory. Our results are two fold. First, we compute the current expectation value in the presence of arbitrary time-dependent and spatially inhomogeneous background electric fields. Bosonization naturally incorporates the renormalization of the current, enabling us to find the fully renormalized result that would be difficult to obtain in the fermion formulation. Second, using full 1+1D QED, we perform fully quantum calculations including the backreaction. Our result shows that the expectation value of the electric field during the discharge satisfies a simple classical nonlinear partial differential equation. Direct comparison between the full quantum result and the semiclassical approximation reveals clear quantitative differences.