* http://arXiv.org/abs/quant-ph/0108121 contains fundamental arguments which lead to the discrete approach (view pdf).

*** http://arXiv.org/abs/quant-ph/0207045 shows the connection of proper time and return probabilities (view pdf).

** To the statistical origin of geometrical appearance: CircumferenceA synthesis of quant-ph/0108121 and quant-ph/0207045 is published in IJMMS 2004:19 (2004) 1003-1023

(More special (probably coincidental) results following from discretization of
the vacuum maxwell equations using the Lattice
software are contained in wqpm1.pdf
which is an updated version of http://arXiv.org/abs/quant-ph/0312188
.)