Monopoles and Lyapunov Exponents in U(1) Lattice Gauge Theory

TL;DR

This paper investigates the chaotic behavior of U(1) lattice gauge fields by decomposing them into monopole and photon parts, analyzing their Lyapunov exponents across phase transitions, and finding monopoles remain chaotic in the continuum.

Contribution

It introduces a method to decompose gauge fields into monopole and photon components and analyzes their Lyapunov exponents through lattice simulations, revealing distinct chaotic properties.

Findings

Monopole density correlates strongly with Lyapunov exponents.

Monopole fields remain chaotic in the continuum.

Photon fields tend to be regular and less chaotic.

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 a strong relation between the sizes of the monopole density and the Lyapunov exponent. Evidence is found that monopole fields stay chaotic in the continuum whereas the photon fields are regular.