For the study of Planck-scale modifications of the energy-momentum dispersion relation, which had been previously focused on the implications for ultrarelativistic (ultrafast) particles, we consider the possible role of experiments involving nonrelativistic particles, and particularly atoms. We extend a recent result establishing that measurements of "atom-recoil frequency" can provide insight that is valuable for some theoretical models. And from a broader perspective we analyze the complementarity of the nonrelativistic and the ultrarelativistic regimes in this research area.

Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framework under the name of relative locality [1] has been proposed as a way to consider Planckian modifications of the relativistic dynamics of particles. We note in this paper that the loss of absolute locality is a general feature of theories beyond Special Relativity with an implementation of a relativity principle. We give an explicit construction of such an implementation and compare it both with the previously mentioned framework of relative locality and the so-

The use of the vacuum lepton pair production process ( ! e À e þ ), a viable reaction for superluminal neutrinos, to put constraints on Lorentz violations requires a dynamical framework. Different choices of dynamical matrix elements and modified dispersion relations for neutrinos, leading to numerical factors differing by 1 order of magnitude in the results for the pair production decay width, are used to show the uncertainties on these constraints.

The symmetry properties of a proposal to go beyond relativistic quantum field theory based on a modification of the commutation relations of fields are identified. Poincaré invariance in an auxiliary spacetime is found in the Lagrangian version of the path integral formulation. This invariance is contrasted with the idea of Doubly (or Deformed) Special Relativity (DSR). This analysis is then used to go from the free theory of a complex field to an interacting field theory.

We propose a general framework to describe Planckian deviations from special relativity compatible with a relativistic principle. They are introduced as the leading corrections in an asymptotic approach to special relativity going beyond the energy power expansion of effective field theories. We discuss the conditions in which these Planckian effects might be experimentally observable in the near future, together with the nontrivial limits of applicability of this asymptotic approach that such a situation would produce, both at the very high (ultraviolet) and the very low (infrared) energy regimes.