  We construct the classical and canonically quantized theories of a massless
scalar field on a background lattice in which the number of points--and hence
the number of modes--may grow in time. To obtain a well-defined theory certain
restrictions must be imposed on the lattice. Growth-induced particle creation
is studied in a two-dimensional example. The results suggest that local mode
birth of this sort injects too much energy into the vacuum to be a viable model
of cosmological mode birth.
