  Massive Klein-Gordon theory is quantized on a timelike hyperplane in
Minkowski space using the framework of general boundary quantum field theory.
In contrast to previous work, not only the propagating sector of the phase
space is quantized, but also the evanescent sector, with the correct physical
vacuum. This yields for the first time a description of the quanta of the
evanescent field alone. The key tool is the novel $\alpha$-K\"ahler
quantization prescription based on a $*$-twisted observable algebra. The
spatial evolution of states between timelike hyperplanes is established and
turns out to be non-unitary if different choices are made for the quantization
ambiguity for initial and final hyperplane. Nevertheless, a consistent notion
of transition probability is established also in the non-unitary case, thanks
to the use of the positive formalism. Finally, it is shown how a conducting
boundary condition on the timelike hyperplane gives rise to what we call the
Casimir state. This is a pseudo-state which can be interpreted as an
alternative vacuum and which gives rise to a sea of particle pairs even in this
static case.
