# Fermion production from real-time lattice gauge theory in the classical-statistical regime

## TL;DR

This paper explores real-time lattice gauge theories with fermions, demonstrating a classical-statistical approach to simulate quantum dynamics and applying it to electron-positron production in QED, highlighting the significance of back-reaction effects.

## Contribution

It introduces a non-perturbative simulation method for fermion production in lattice gauge theories using classical-statistical ensembles, capturing genuine quantum effects.

## Key findings

- Successful simulation of electron-positron pair production in 3D QED
- Demonstrated the importance of back-reaction of fermions on gauge fields
- Validated the approach against analytic solutions for constant backgrounds

## Abstract

We investigate the real-time dynamics of U(1) and SU(N) gauge theories coupled to fermions on a lattice. While real-time lattice gauge theory is not amenable to standard importance sampling techniques, for a large class of time-dependent problems the quantum dynamics can be accurately mapped onto a classical-statistical ensemble. We illustrate the genuine quantum contributions included in this description by giving a diagrammatic representation in a series expansion. The non-perturbative simulation method is then applied to electron-positron production in quantum electrodynamics in three spatial dimensions. We compare to analytic results for constant background field and demonstrate the importance of back-reaction of the produced fermion pairs on the gauge fields.