Observables of Lattice Gauge Theory in Minkowski Space

TL;DR

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

Contribution

It introduces a decomposition of U(1) gauge fields into monopole and photon parts and analyzes their Lyapunov spectra, revealing distinct chaotic behaviors.

Findings

Monopole fields share the same Lyapunov exponent as the original field.

Monopole fields remain chaotic in the continuum.

Photon fields tend to be regular in the continuum.

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. Evidence is found that monopole fields stay chaotic in the continuum whereas the photon fields are regular. First results are presented for the full spectrum of Lyapunov exponents of the U(1) gauge system.