  This paper is devoted to the computation of discrete propagators in
two-dimensional crystals and their application to a number of time dependent
problems. The methods to compute such kernels are provided by a tight-binding
representation of Dirac matrices and the generalizations of Bessel functions.
Diffusive effects of point-like distributions on crystalline sheets are studied
in a second quantization scheme. In the last part, a compendium of propagators
is presented. The cases of square, triangular and hexagonal arrays are covered.
