Abstract:
Lorentz violation at high energies might lead to non linear dispersion relations for the fundamental particles. We analyze observational constraints on these without assuming any a priori equality between the coefficients determining the amount of Lorentz violation for different particle species. We focus on constraints from three high energy processes involving photons and electrons: photon decay, photo-production of electron-positron pairs, and vacuum Cerenkov radiation. We find that cubic momentum terms in the dispersion relations are strongly constrained.

Abstract:
The time delays between gamma-rays of different energies from extragalactic sources have often been used to probe quantum gravity models in which Lorentz symmetry is violated. It has been claimed that these time delays can be explained by or at least put the strongest available constraints on quantum gravity scenarios that cannot be cast within an effective field theory framework, such as the space-time foam, D-brane model. Here we show that this model would predict too many photons in the ultra-high energy cosmic ray flux to be consistent with observations. The resulting constraints on the space-time foam model are much stronger than limits from time delays and allow for Lorentz violations effects way too small for explaining the observed time delays.

Abstract:
Recent observations of ultra high energy cosmic rays and gamma rays suggest that there are small violations of Lorentz symmetry. If there were no such violations, then the GZK cut off would hold and cosmic rays with energy $\sim 10^{20}eV$ or higher would not be reaching the earth. However some such events seem to have been observed. This has lead to phenomenological models in which there is a small violation of the Lorentz symmetry or the velocity of light. However recent Quantum Gravity and String Theory approaches which no longer consider a differentiable spacetime manifold already predict such violations. Similarly there are other theoretical reasons which also point to this. We briefly discuss the various possibilities.

Abstract:
A consistent theory of quantum gravity (QG) at Planck scale almost sure contains manifestations of Lorentz local symmetry violations (LV) which may be detected at observable scales. This can be effectively described and classified by models with nonlinear dispersions and related Finsler metrics and fundamental geometric objects (nonlinear and linear connections) depending on velocity/ momentum variables. We prove that the trapping brane mechanism provides an accurate description of gravitational and matter field phenomena with LV over a wide range of distance scales and recovering in a systematic way the general relativity (GR) and local Lorentz symmetries. In contrast to the models with extra spacetime dimensions, the Einstein-Finsler type gravity theories are positively with nontrivial nonlinear connection structure, nonholonomic constraints and torsion induced by generic off-diagonal coefficients of metrics, and determined by fundamental QG and/or LV effects.

Abstract:
Three symmetry constraints on the CP violations in QCD are discussed in this paper. In order to generate CP violating observables from QCD, these constraints require: (1) spontaneous chiral symmetry breaking, (2) explicit chiral symmetry breaking, e.g., finite quark masses, (3) $U_A(1)$ anomaly, in addition to a nonzero $\thetabar$ parameter. A pictorial illustration is used to unify and elucidate these constraints and indicate a dual relation between quark mass and the quark condensate. Based on the symmetry constraints, a dynamical suppression scenario to solve the strong CP problem within QCD is examined. We conclude that a solution of the strong CP problem has to involve physics beyond the standard model.

Abstract:
Relativistic Invariance might be modified by Quantum Gravity effects. The interesting point which emerged in the last fifteen years is that remnants of possible Lorentz Invariance Violations could be present at energies much lower than their natural scale, and possibly affect Ultra High Energy Cosmic Rays phenomena. We discuss their status in the view of recent data from the Pierre Auger Observatory.

Abstract:
The framework of relativistic quantum-field theories requires Lorentz Invariance. Many theories of quantum gravity, on the other hand, include violations of Lorentz Invariance at small scales and high energies. This generates a lot of interest in establishing limits on such effects, and, if possible, observing them directly. Gamma-ray observatories provide a tool to probe parts of the parameter space of models of Lorentz Invariance Violation that is not accessible in terrestrial laboratories and man-made accelerators. Transients, especially gamma-ray bursts, are a particularly promising class of events to search for such phenomena. By combining cosmological distances with high energy emission and short duration, emitting photons up to 30 GeV in less than a second, one can measure the energy dependence of the speed of photons to one part in $10^{16}$. We will discuss the potential of HAWC to detect effects of the violation of Lorentz Invariance and place its sensitivity in the context of existing limits.

Abstract:
Binary pulsars are excellent laboratories to test the building blocks of Einstein's theory of General Relativity. One of these is Lorentz symmetry which states that physical phenomena appear the same for all inertially moving observers. We study the effect of violations of Lorentz symmetry in the orbital evolution of binary pulsars and find that it induces a much more rapid decay of the binary's orbital period due to the emission of dipolar radiation. The absence of such behavior in recent observations allows us to place the most stringent constraints on Lorentz violation in gravity, thus verifying one of the cornerstones of Einstein's theory much more accurately than any previous gravitational observation.

Abstract:
Planetary ephemerides are a very powerful tool to constrain deviations from the theory of General Relativity using orbital dynamics. The effective field theory framework called the Standard-Model Extension (SME) has been developed in order to systematically parametrize hypothetical violations of Lorentz symmetry (in the Standard Model and in the gravitational sector). In this communication, we use the latest determinations of the supplementary advances of the perihelia and of the nodes obtained by planetary ephemerides analysis to constrain SME coefficients from the pure gravity sector and also from gravity-matter couplings. Our results do not show any deviation from GR and they improve current constraints. Moreover, combinations with existing constraints from Lunar Laser Ranging and from atom interferometry gravimetry allow us to disentangle contributions from the pure gravity sector from the gravity-matter couplings.

Abstract:
Analogue models of gravity have provided an experimentally realizable test field for our ideas on quantum field theory in curved spacetimes but they have also inspired the investigation of possible departures from exact Lorentz invariance at microscopic scales. In this role they have joined, and sometime anticipated, several quantum gravity models characterized by Lorentz breaking phenomenology. A crucial difference between these speculations and other ones associated to quantum gravity scenarios, is the possibility to carry out observational and experimental tests which have nowadays led to a broad range of constraints on departures from Lorentz invariance. We shall review here the effective field theory approach to Lorentz breaking in the matter sector, present the constraints provided by the available observations and finally discuss the implications of the persisting uncertainty on the composition of the ultra high energy cosmic rays for the constraints on the higher order, analogue gravity inspired, Lorentz violations.