The construction of effective Hamiltonians describing corrections to flat
space particle dynamics arising from the granularity of space at very short
distances is discussed in the framework of an heuristic approach to the
semiclassical limit of loop quantum gravity. After some general motivation of
the subject, a brief non-specialist introduction to the basic tools employed in
the loop approach is presented. The heuristical semiclassical limit is
subsequently defined and the application to the case of photons and spin 1/2
fermions is described. The resulting modified Maxwell and Dirac Hamiltonians,
leading in particular to Planck scale corrections in the energy-momentum
relations, are presented. Alternative interpretations of the results and their
limitations, together with other approaches are briefly discussed along the
text. Three topics related to the above methods are reviewed: (1) The
determination of bounds to the Lorentz violating parameters in the fermionic
sector, obtained from clock comparison experiments.(2) The calculation of
radiative corrections in preferred frames associated to space granularity in
the framework of a Yukawa model for the interactions and (3) The calculation of
synchrotron radiation in the framework of the Myers-Pospelov effective theories
describing Lorentz invariance violations, as well as a generalized approach to
radiation in Planck scale modified electrodynamics. The above exploratory
results show that quantum gravity phenomenology provides observational guidance
in the construction of quantum gravity theories and opens up the possibility of
probing Planck scale physics.Comment: 49 pages, 6 figures and 4 tables. Extended version of the talk given
at the 339-th WE-Heraeus-Seminar: Special Relativity, will it survive the
next 100 years?, Potsdam, february 200