Simulating hot Abelian gauge dynamics

TL;DR

This paper develops a local Hamiltonian formulation for simulating the non-equilibrium dynamics of Abelian gauge theories, enabling detailed numerical studies of phase transitions and defect formation.

Contribution

It introduces a local, Hamiltonian approach to simulate Abelian gauge field dynamics, facilitating numerical analysis of phase transitions and initial condition effects.

Findings

The local Hamiltonian formulation enables efficient numerical simulations.

Simulations agree well with analytical results.

Different initial conditions lead to qualitatively different dynamics.

Abstract

The time evolution of soft modes in a quantum gauge field theory is to first approximation classical, but the equations of motion are non-local. We show how they can be written in a local and Hamiltonian way in an Abelian theory, and that this formulation is particularly suitable for numerical simulations. This makes it possible to simulate numerically non-equilibrium processes such as the phase transition in the Abelian Higgs model and and to study, for instance, bubble nucleation and defect formation. Such simulations would also help to understand phase transitions in more complicated gauge theories. Moreover, we show that the existing analytical results for the time-evolution in a pure-gauge theory correspond to a special class of initial conditions and that different initial conditions can lead to qualitatively different behavior. We compare the results of the simulations to analytical calculations and find an excellent agreement.