  We show that a system of a domain wall coupled to a scalar field has static
negative energy density at certain distances from the domain wall. This system
provides a simple, explicit example of violation of the averaged weak energy
condition and the quantum inequalities by interacting quantum fields. Unlike
idealized systems with boundary conditions or external background fields, this
calculation is implemented precisely in renormalized quantum field theory with
the energy necessary to support the background field included
self-consistently.
