Monopoles in Real Time for Classical U(1) Gauge Field Theory

TL;DR

This paper investigates the real-time dynamics of monopoles in U(1) gauge fields, revealing that monopoles are created and annihilated in pairs, with their chaotic behavior characterized by Lyapunov exponents.

Contribution

It demonstrates that monopoles in U(1) gauge theory share the same Lyapunov exponent as the full field and provides real-time evidence of monopole pair creation and annihilation.

Findings

Monopoles carry the same Lyapunov exponent as the original field.

Monopoles are created and annihilated in pairs over time.

Monopole dynamics are analyzed across the phase transition.

Abstract

U(1) gauge fields are decomposed into a monopole and photon part across the phase transition from the confinement to the Coulomb phase. We analyze the leading Lyapunov exponents of such gauge field configurations on the lattice which are initialized by quantum Monte Carlo simulations. We observe that the monopole field carries the same Lyapunov exponent as the original U(1) field. As a long awaited result, we show that monopoles are created and annihilated in pairs as a function of real time in excess to a fixed average monopole number.