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

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.