  Polymer quantization is a non-standard approach to quantizing a classical
system inspired by background independent approaches to quantum gravity such as
loop quantum gravity. When applied to field theory it introduces a
characteristic polymer scale at the level of the fields classical configuration
space. Compared with models with space-time discreteness or non-commutativity
this is an alternative way in which a characteristic scale can be introduced in
a field theoretic context. Motivated by this comparison we study here
localization and diffusion properties associated with polymer field observables
and dispersion relation in order to shed some light on the novel physical
features introduced by polymer quantization. While localization processes seems
to be only mildly affected by polymer effects, we find that polymer diffusion
differs significantly from the "dimensional reduction" picture emerging in
other Planck-scale models beyond local quantum field theory.
