Urrutia, L. F. Corrections to flat-space particle dynamics arising from space granularity. (English) Zbl 1151.83302 Ehlers, Jürgen (ed.) et al., Special relativity. Will it survive the next 101 years? Papers based on the presentations at the 271st WE-Heraeus seminar on special relativity, Potsdam, Germany, February 13–18, 2005. Berlin: Springer (ISBN 3-540-34522-1/hbk). Lecture Notes in Physics 702, 299-345 (2006). Summary: 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.For the entire collection see [Zbl 1140.83008]. Cited in 2 Documents MSC: 83A05 Special relativity 83C10 Equations of motion in general relativity and gravitational theory PDFBibTeX XMLCite \textit{L. F. Urrutia}, Lect. Notes Phys. 702, 299--345 (2006; Zbl 1151.83302) Full Text: DOI arXiv