Effective Lorentz Invariance Research Articles

Constraining Lorentz Invariance Violation Using the Crab Pulsar Emission Observed up to TeV Energies by MAGIC

Abstract Spontaneous breaking of Lorentz symmetry at energies on the order of the Planck energy or lower is predicted by many quantum gravity theories, implying non-trivial dispersion relations for the photon in vacuum. Consequently, gamma-rays of different energies, emitted simultaneously from astrophysical sources, could accumulate measurable differences in their time of flight until they reach the Earth. Such tests have been carried out in the past using fast variations of gamma-ray flux from pulsars, and more recently from active galactic nuclei and gamma-ray bursts. We present new constraints studying the gamma-ray emission of the galactic Crab Pulsar, recently observed up to TeV energies by the Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC) collaboration. A profile likelihood analysis of pulsar events reconstructed for energies above 400 GeV finds no significant variation in arrival time as their energy increases. Ninety-five percent CL limits are obtained on the effective Lorentz invariance violating energy scale at the level of ( ) for a linear, and ( ) for a quadratic scenario, for the subluminal and the superluminal cases, respectively. A substantial part of this study is dedicated to calibration of the test statistic, with respect to bias and coverage properties. Moreover, the limits take into account systematic uncertainties, which are found to worsen the statistical limits by about 36%–42%. Our constraints would have been much more stringent if the intrinsic pulse shape of the pulsar between 200 GeV and 400 GeV was understood in sufficient detail and allowed inclusion of events well below 400 GeV.

Effective theory and breakdown of conformal symmetry in a long-range quantum chain

We deal with the problem of studying the symmetries and the effective theories of long-range models around their critical points. A prominent issue is to determine whether they possess (or not) conformal symmetry (CS) at criticality and how the presence of CS depends on the range of the interactions. To have a model, both simple to treat and interesting, where to investigate these questions, we focus on the Kitaev chain with long-range pairings decaying with distance as power-law with exponent α. This is a quadratic solvable model, yet displaying non-trivial quantum phase transitions. Two critical lines are found, occurring respectively at a positive and a negative chemical potential. Focusing first on the critical line at positive chemical potential, by means of a renormalization group approach we derive its effective theory close to criticality. Our main result is that the effective action is the sum of two terms: a Dirac action SD, found in the short-range Ising universality class, and an “anomalous” CS breaking term SAN. While SD originates from low-energy excitations in the spectrum, SAN originates from the higher energy modes where singularities develop, due to the long-range nature of the model. At criticality SAN flows to zero for α>2, while for α<2 it dominates and determines the breakdown of the CS. Out of criticality SAN breaks, in the considered approximation, the effective Lorentz invariance (ELI) for every finite α. As α increases such ELI breakdown becomes less and less pronounced and in the short-range limit α→∞ the ELI is restored. In order to test the validity of the determined effective theory, we compared the two-fermion static correlation functions and the von Neumann entropy obtained from them with the ones calculated on the lattice, finding agreement. These results explain two observed features characteristic of long-range models, the hybrid decay of static correlation functions within gapped phases and the area-law violation for the von Neumann entropy. The proposed scenario is expected to hold in other long-range models displaying quasiparticle excitations in ballistic regime. From the effective theory one can also see that new phases emerge for α<1. Finally we show that at every finite α the critical exponents, defined as for the short-range (α→∞) model, are not altered. This also shows that the long-range paired Kitaev chain provides an example of a long-range model in which the value of α where the CS is broken does not coincide with the value at which the critical exponents start to differ from the ones of the corresponding short-range model. At variance, for the second critical line, having negative chemical potential, only SAN (SD) is present for 1<α<2 (for α>2). Close to this line, where the minimum of the spectrum coincides with the momentum where singularities develop, the critical exponents change where CS is broken.

Electromagnetism as an emergent phenomenon: a step-by-step guide

We give a detailed description of electrodynamics as an emergent theory from condensed-matter-like structures, not only per se but also as a warm-up for the study of the much more complex case of gravity. We concentrate on two scenarios that, although qualitatively different, share some important features with the idea of extracting the basic generic ingredients that give rise to emergent electrodynamics and, more generally, to gauge theories. We start with Maxwellʼs mechanical model for electrodynamics, where Maxwellʼs equations appear as dynamical consistency conditions. We next take a superfluid 3He-like system as representative of a broad class of fermionic quantum systems whose low-energy physics reproduces classical electrodynamics (Dirac and Maxwell equations as dynamical low-energy laws). An important lesson that can be derived from both analyses is that the vector potential has a microscopic physical reality and only in the low-energy regime is this physical reality blurred in favor of gauge invariance, which in addition turns out to be secondary to effective Lorentz invariance.

Soft gravitational effects in Kadanoff-Baym approach

In de Sitter space, the gravitational fluctuation at the super-horizon scale may make physical quantities time dependent by breaking the de Sitter symmetry. We adopt the Kadanoff-Baym approach to evaluate soft gravitational effects in a matter system at the sub-horizon scale. This investigation proves that only the local terms contribute to the de Sitter symmetry breaking at the one-loop level. The IR singularities in the non-local terms cancel after summing over degenerate states between real and virtual processes. The corresponding IR cut-off is given by the energy resolution like QED. Since the energy resolution is physical and independent of cosmic evolution, the non-local contributions do not induce the de Sitter symmetry breaking. We can confirm that soft gravitational effects preserve the effective Lorentz invariance.

Scheme dependence of quantum gravity on de Sitter background

We extend our investigation of the IR effects on the local dynamics of matter fields in quantum gravity. Specifically we clarify how the IR effects depend on the change of the quantization scheme: different parametrization of the metric and the matter field redefinition. Conformal invariance implies effective Lorentz invariance of the matter system in de Sitter space. An arbitrary choice of the parametrization of the metric and the matter field redefinition does not preserve the effective Lorentz invariance of the local dynamics. As for the effect of different parametrization of the metric alone, the effective Lorentz symmetry breaking term can be eliminated by shifting the background metric. In contrast, we cannot compensate the matter field redefinition dependence by such a way. The effective Lorentz invariance can be retained only when we adopt the specific matter field redefinitions where all dimensionless couplings become scale invariant at the classical level. This scheme is also singled out by unitarity as the kinetic terms are canonically normalized.

Synchrotron radiation in Lorentz-violating electrodynamics: The Myers-Pospelov model

We develop a detailed analysis of synchrotron radiation in the effective Lorentz invariance violating (LIV) model of Myers-Pospelov, considering explicitly both the dynamics of the charge producing the radiation and the dynamics of the electromagnetic field itself. Within the radiation approximation we compute exact expressions in the LIV parameters for the electric and magnetic fields, the angular distribution of the power spectrum, the total emitted power in the $m$th harmonic and the polarization. We also perform expansions of the exact results in terms of the LIV parameters to identify the dominant effects and study the main features of the high energy limit of the spectrum. A very interesting consequence is the appearance of rather unexpected and large amplifying factors associated with the LIV effects, which go along with the usual contributions of the expansion parameter. This opens up the possibility of looking for astrophysical sources where these amplifying factors are important to further explore the constraints imposed upon the LIV parameters by synchrotron radiation measurements. We briefly sketch some phenomenological applications in the case of supernova remnants and gamma ray bursts.

Synchrotron radiation in Myers–Pospelov effective electrodynamics

In the framework of the classical effective Lorentz invariance violating (LIV) model of Myers–Pospelov, we present a complete calculation of the synchrotron radiation produced by a circularly moving charge in the rest frame of the model. Within the full far-field approximation we compute exact expressions for the electric and magnetic fields, the angular distribution of the power spectrum and the total emitted power in the mth harmonic. We also perform an expansion of the latter quantity in terms of the electromagnetic LIV parameter and calculate the average degree of circular polarization to first order in such a parameter. In both cases we find, under adequate circumstances, the appearance of rather unexpected and large amplifying factors, which go together with the otherwise negligible naive expansion parameter. This opens up the possibility of selecting astrophysical sources where these amplifying factors are important, to explore further constraints imposed upon the LIV parameters by synchrotron radiation measurements.