  At second order in perturbation theory, we find the ground states of the
$\phi^4$ double-well quantum field theory in 1+1 dimensions. The operators
which create these ground states from the free vacuum are constructed
explicitly at this order, as is the operator which interpolates between the
ground states. As a warm up we perform the analogous calculation in quantum
mechanics, where the true ground state is unique but in perturbation theory
there are also two ground states.
