Loop Quantum Gravity Induced Corrections to Fermion Dynamics in Flat Space

Loop Quantum Gravity (LQG) has provided a highly successful approach to deal with the old problem of constructing a quantum version of Einstein general relativity. Among its predictions we singularize the property that the area and volume operators are quantized in the corresponding units of the Planck length lP . 1 In this way, a continuum description of space should be considered only as an approximation valid for length scales L >> lP . The granular structure of space at short distances poses at least two interesting problems certainly tied to each other. On one hand there is the question of whether or not such granular structure will induce modifications to standard particle dynamics in flat space, for example. A most promising observational consequence of these corrections is the modification of the standard energy-momentum relations for particles. The analogy with particle propagation in a lattice crystal, for example, suggests that modifications will indeed arise. Secondly, since that granular structure incorporates the notion of a minimum (maximum) length (momentum), another important related issue is how these corrections would affect Einstein special relativity principle.