A microscopic semiclassical confining field equation for $U(1)$ lattice   gauge theory in 2+1 dimensions
  We present a semiclassical nonlinear field equation for the confining field in 2+1--dimensional $U(1)$ lattice gauge theory (compact QED). The equation is derived directly from the underlying microscopic quantum Hamiltonian by means of truncation. Its nonlinearities express the dynamic creation of magnetic monopole currents leading to the confinement of the electric field between two static electric charges. We solve the equation numerically and show that it can be interpreted as a London relation in a dual superconductor. 
Christoph Best and Andreas Schaefer (Frankfurt, Germany)