  We get deeper understanding of the role played by boundary conditions in
quantum field theory, by studying the structure of a scalar massless quantum
field theory bounded by two one dimensional planar crystal plates. The system
can also be understood as a massless scalar confined to propagate in the
surface of a finite cylinder. We classify the most general type of regular
behaved boundary conditions that the quantum field can satisfy, in accordance
with the unitarity principle of quantum field theory. Also, we characterize the
frequency spectrum for each quantum field theory, by computing the holomorphic
spectral function. The spectral function is the starting point to compute the
Casimir energy as a global function over the space of allowed boundary
conditions for the quantum field theory.
