Quantum Chameleons
  We initiate a quantum treatment of chameleon-like particles, deriving
classical and quantum forces directly from the path integral. It is found that
the quantum force can potentially dominate the classical one by many orders of
magnitude. We calculate the quantum chameleon pressure between infinite plates,
which is found to interpolate between the Casimir and the integrated
Casimir-Polder pressures, respectively in the limits of full screening and no
screening. To this end we calculate the chameleon propagator in the presence of
an arbitrary number of one-dimensional layers of material. For the E\"ot-Wash
experiment, the five-layer propagator is used to take into account the
intermediate shielding sheet, and it is found that the presence of the sheet
enhances the quantum pressure by two orders of magnitude. As an example of
implication, we show that in both the standard chameleon and symmetron models,
large and previously unconstrained regions of the parameter space are excluded
once the quantum pressure is taken into account.
