CPT and Lorentz Symmetry

The following sections are included:

• Preface
• Contents

The BASE collaboration at the Antiproton Decelerator facility of CERN compares the fundamental properties of protons and antiprotons using advanced Penning-trap systems. In previous measurement campaigns, we measured the magnetic moments of the proton and the antiproton, reaching (sub-)parts-in-a-billion fractional uncertainty. In the latest campaign, we have compared the proton and antiproton charge-to-mass ratios with a fractional uncertainty of 16 parts in a trillion. In this contribution, we give an overview of the measurement campaign, and detail how its results are used to constrain nine spin-independent coefficients of the Standard-Model Extension in the proton and electron sector.

GINGER (Gyroscopes IN GEneral Relativity), based on an array of large-dimension ring-laser gyroscopes, is aiming at measuring in the Gran Sasso underground laboratory the Earth’s angular velocity with unprecedented sensitivity in order to record the general-relativity effects on top of the Earth crust; one part in 10⁹ on the Earth’s surface is the goal to access the signals expected by general relativity, due to the de Sitter and Lense–Thirring effects. This target is also valuable for Lorentz-violation in the gravity sector. GINGER is an multi-disciplinary project. Being attached to the Earth’s crust, it will provide useful data for geophysical investigation, and it will be one of the instruments in the recently proposed multi-components geophysical observatory of Gran Sasso. It is expected that the realization of GINGER will take 18 months, and it will take 3 years to reach the relative sensitivity of one part in 10¹¹.

Effective field theories that allow for the possibility of Lorentz violation may sometimes also include redundancies of description in their actions. When this kind of redundancy exists, different renormalization prescriptions can lead to differing expressions for the renormalization group β-functions at one-loop order. However, the renormalization group scaling of physically observable quantities remains unambiguous, as it should.

A first result related to a CPT test in the decay of ortho-positronium based on data collected by means of the J-PET detector is already available, and a new test of CP symmetry is under investigation. Both results are based on the determination of angular correlations between momenta of gamma rays and other vector properties of the investigated system. Here, arguments for the possible usage of data collected by the J-PET group to test CPT symmetry within the Standard-Model Extension framework are shortly presented.

This proceedings contribution outlines the current structure of the gravity sector of the Standard-Model Extension and summarizes recent progress in gravitational wave analysis.

This contribution to the CPT’22 meeting provides a brief review of some concepts in Lorentz and CPT violation.

A central issue in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale of the QCD running coupling. The purpose of the running coupling in any gauge theory is to sum all terms involving the β function; in fact, when the renormalization scale is set properly, all non-conformal β terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory, i.e., the corresponding theory with β = 0. The resulting scale-fixed predictions using the “Principle of Maximum Conformality” (PMC) are independent of the choice of renormalization scheme—a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale-setting in the Abelian limit. The PMC is also the theoretical principle underlying the BLM procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors n_F in the QCD β function is also correctly determined. The elimination of the renormalization scale ambiguity and the scheme dependence using the PMC not only increases the precision of QCD tests, but it also increases the sensitivity of collider experiments to new physics beyond the SM…

The ASACUSA collaboration is developing a polarized beam of antihydrogen atoms to precisely determine the ground-state hyperfine structure for studies of CPT and Lorentz invariance. Using a beam of ordinary hydrogen, measurements of both the σ and π transition have been performed, investigating orientation-dependent SME coefficients. Furthermore a first hyperfine experiment with a beam of deuterium is being prepared.

Violations of Lorentz invariance can affect gravitational waves through both dispersion and birefringence. This contribution to the CPT’22 proceedings summarizes the effects of gauge-invariant Lorentz violations within the Standard-Model Extension.

Cosmic rays and air showers at ultrahigh energy are unique tools to test the validity of Lorentz invariance. A brief overview is given on such tests focusing on isotropic, non-birefringent Lorentz violation in the photon sector. Based on the apparent absence of vacuum Cherenkov radiation and photon decay, the Lorentz-violating parameter κ is bounded to −0.6 · 10⁻²⁰ < κ < 6 · 10⁻²⁰ (98% CL). We report an updated limit from cosmic-ray photon observations and preliminary results on testing vacuum Cherenkov radiation in air showers.

In this CPT ’22 conference proceedings, an overview is given of recent experimental limits placed on Lorentz and CPT violation in the Standard-Model Extension. The approximately two dozen experimental publications added to the Data Tables for Lorentz and CPT Violation in the last three years are summarized. The limits on coefficients for Lorentz violation cover the quantum electrodynamics sectors, the Standard Model, and the gravity sector.

We consider Lorentz-symmetry properties of the ghost-free massive gravity theory proposed by de Rham, Gabadadze, and Tolley. In particular, we present potentially observable effects in gravitational-wave propagation and in Newton’s law, including Lorentz-violating signals.

Lorentz invariance is a fundamental symmetry of spacetime underpinning the Standard Model and our understanding of high-energy phenomena in particle physics. However, beyond the quantum gravity scale, we expect the Standard Model to be replaced with a more fundamental, covariant theory giving a quantum description of gravity. The effective theory arising from this theory can break Lorentz invariance and thus predicts observables that exhibit low-energy manifestations of Lorentz violation. In particular, these observables could be a subleading contribution to neutrino oscillations and could therefore explain anomalous flavor measurements. The Standard-Model Extension formalism describing such an effective theory predicts terms whose characteristic oscillation length becomes significant at atmospheric-neutrino energies accessible by the IceCube Neutrino Observatory. We describe past measurements and efforts to extend these using ten years of data along with a new energy reconstruction to study ν_μ disappearance.

By utilizing the quadratic dependency of the interferometry phase on time, the Hannover Very Long Baseline Atom Interferometer facility (VLBAI) aims for sub nms⁻² gravity measurement sensitivity. With its 10 m vertical baseline, the VLBAI offers promising prospects in testing fundamental physics at the interface between quantum mechanics and general relativity. Here we discuss the challenges imposed by controlling the VLBAI’s magnetic and gravitational environment and report on their effect on the device’s accuracy. Within the inner 8 m of the magnetic shield, residual magnetic field gradients expect to cause a bias acceleration of only 6 × 10⁻¹⁴ ms⁻² while we evaluate the bias shift due to the facility’s non-linear gravity gradient to 2.6 nms⁻². The model allows the VLBAI facility to be a reference to other mobile devices for calibration purposes with an uncertainty below the 10 nms⁻² level.

We summarize recent work dealing with the characterization of effective actions giving the electromagnetic response of some topological materials, arising from their microscopic structure. The case of weakly tilted Weyl semimetals in the limit of zero temperature, but nonzero chemical potential, is presented as a subset of a specific choice of terms in the fermionic sector of the SME.

Direct tests of T, CP, CPT symmetries in transitions using entangled neutral kaons produced at a ϕ-factory are briefly reviewed.

This presentation discusses some of the signals for Lorentz violation potentially observable in atomic spectroscopy and clock-comparison experiments. The emphasis of the discussion is on how the angular-momentum quantum numbers of the states involved in the transition determine the properties of the possible sidereal variation of the transition frequency.

Many new linearized coefficients for Lorentz violation are discovered in our recent work on the construction of a generic Lorentz-violating effective field theory in curved spacetime. The new coefficients can be constrained by experiments in weak gravity fields. In this work, we compare experiments in different gravitational potentials and study three types of gravity-related experiments: free-fall, gravitational interferometer, and gravitational bound-state experiments. First constraints on the new coefficients for Lorentz violation are extracted from those experiments.

Searches for empirical clues beyond Einstein’s General Relativity are crucial to understand gravitation and spacetime. Radio pulsars have been playing an important role in testing gravity theories since the 1970s. Because radio timing of binary pulsars is very sensitive to changes in the orbital dynamics, small deviations from what General Relativity predicts can be captured or constrained. In this sense, the gravity sector on the Standard-Model Extension was constrained tightly with a set of pulsar systems. Moreover, compact objects like pulsars may develop nonperturbative deviations from General Relativity in some specific alternative gravity theories, thus radio pulsars also provide rather unique testbeds in the strong-gravity regime.

In this contribution, our efforts consist in presenting and discussing the status of a paper in progress we are working on to investigate how non-linear electromagnetic effects couple to the parameters that signal Lorentz-symmetry violation. Here, we realize Lorentz-symmetry violation by means of a specific model, namely Carroll–Field–Jackiw’s. We set the formulation by considering a general non-linear photonic Lagrangian (written in terms of the Lorentz-invariant bilinears in the field strength) that may be coupled to different operators that carry the message of Lorentz-symmetry violation. We expect that our efforts might be of interest in connection with the experiments carried out with the existing super-intense LASERs based on chirped-pulse amplification.

I will discuss the issue of gravitational studies of the Positronium system, with regards to the approach followed by the QUPLAS interferometric experiment. The physical interest will be discussed and the measurement strategy will be outlined. Some of the most relevant problems will be highlighted.

Astrophysical polarization measurements provide some of the strongest constraints on the photon sector of the non-minimal Standard-Model Extension. This paper reviews some recent results obtained by combining optical linear and circular polarization data from a large number of astrophysical objects.

We review the status of tests of spacetime symmetries with gravity. Recent theoretical and experimental work has involved gravitational-wave signals, precision solar-system tests, and sensitive laboratory tests searching for violations of spacetime symmetries. We present some new theoretical results relevant for short-range gravity tests, with features of multiple length scales, and possible large non-Newtonian forces at short distances.

We review the propagation of electromagnetic waves in continuous matter in the presence of Lorentz-violating terms. First, we briefly discuss classical electrodynamics with regard to optical properties of a dielectric medium exhibiting the Chiral Magnetic Effect. Such a medium can be modeled by Maxwell–Carroll–Field–Jackiw theory. Second, we describe the impact of CPT-odd terms of mass dimensions three and five, respectively, on electromagnetic propagation in continuous matter. Birefringence and absorption are analyzed in the scenarios investigated. Our findings provide new insights into the interplay between classical field theory and optical effects in matter.

Lorentz-violating background fields can naturally arise from nontrivial expectation values of new dynamical tensor fields added to the Standard Model (spontaneous breaking). Alternatively, they can be introduced by postulating non-dynamical tensors that are included directly in the action (explicit breaking). Torsion provides a natural field that can be treated in either way. This talk will compare and contrast the two approaches in a very simple model that includes a metric and a totally antisymmetric torsion term.

Penning-trap experiments on single protons or antiprotons have proven to be an excellent tool to test the fundamental CPT symmetry in the baryonic sector. Here we discuss experimental prospects to cool single ⁹Be⁺ ions to their motional ground state by using laser cooling in order to manipulate single protons or antiprotons for CPT experiments in Penning traps.

This chapter of the proceedings for the Ninth Meeting on CPT and Lorentz Symmetry is dedicated to the Hamiltonian formulation of the minimal gravitational Standard-Model Extension. Some theoretical questions associated with the latter shall be reviewed. First, we recall the properties of the Hamiltonian, which was computed elsewhere, and discuss how it is linked to the modified Einstein equations. Second, we describe how the covariant and Hamiltonian formulations are shown to be consistent with each other.

Linearized gravity in the Very Special Relativity is considered. A graviton mass m_g ≠ 0 maintaining gauge invariance and the usual relativistic dispersion relation is allowed. We show that this graviton has only two physical degrees of freedom, and we compare some results for classical gravitational waves with those in Very Special Relativity using the geodesic-deviation equation. We find that the ratios between Very Special Relativity effects and classical ones are proportional to (m_g/E)² with E the graviton energy. For waves detectable by the interferometers LIGO and VIRGO, this ratio is at most 10⁻²⁰. For waves with lower frequencies in the range of future detectors, like LISA, the ratio increases significantly to 10⁻¹⁰. This combined with the anisotropic nature of Very Special Relativity phenomena may lead to observable effects.

We have realized an atom interferometer that probes gravitational potentials by holding, rather than dropping, atoms. Up to one minute of coherence times are realized by suspending the spatially separated atomic wave packets in an optical lattice that is mode-filtered by an optical cavity. This trapped configuration suppresses phase variance due to vibrations by four to five orders of magnitude, overcoming the dominant noise source in atom-interferometric gravimeters. Recent progress in characterizing and reducing interferometer decoherence led to major increases in coherence and precision, paving the way to measurements of dark-energy candidates and probes of the quantum nature of gravity through measuring the gravity of source masses with record precision and spatial resolution.

It is known that the Hamiltonian describing the low-energy phase of three-dimensional Weyl semimetals has a direct correspondence to Lorentz-violating QED in 3+1 dimensions. We discuss that, in the massive case, the symmetries of the Hamiltonian alone do not uniquely determine the Lagrangian due to redundancies in the action under field redefinitions. This motivates a more comprehensive approach to studying Dirac and Weyl semimetals using relativistic effective field theory. As an application, we discuss the leading-order effects to transport phenomena in Dirac semimetals in the perturbative regime of the Standard-Model Extension.

In this work, we show that surface terms, which map dependence on regularization, can be fixed requiring momentum-routing invariance of tadpoles or diagrams with more external legs. This condition makes the Lorentz-violating terms induced by quantum corrections determined and unique.

As a basic symmetry of Einstein’s theory of special relativity, Lorentz invariance has withstood very strict tests. But there are still motivations for such tests. Firstly, many theories of quantum gravity suggest violations of Lorentz invariance at the Planck energy scale. Secondly, even minute deviations from Lorentz symmetry can accumulate as particles travel across large distances, leading to detectable effects at attainable energies. Thanks to their long baselines and high-energy emission, astrophysical observations provide sensitive tests of Lorentz invariance in the photon sector. In this paper, I briefly introduce astrophysical methods that we adopted to search for Lorentz-violating signatures, including vacuum dispersion and vacuum birefringence.

In this talk, we give a short overview of recent work on cosmological solutions within the SME’s gravitational sector under the assumption of explicit spacetime-symmetry breaking. We show that for the special case of timelike diffeomorphism breaking, the resulting Friedmann equations can be written as standard FLRW cosmology with added dynamical dark energy, and we discuss primordial gravitational waves in the context of this model.

In this work, I outline recent efforts to constrain models based on GUPs using limits on coefficients of the Standard-Model Extension. Two main results are reported: (1) bounds on isotropic GUP models are improved by a factor of 10⁷ compared to previous spectroscopic bounds; and (2) anisotropic GUP models are established and also constrained.

A brief recap is given of issues that can occur when fixed nondynamical backgrounds that explicitly break diffeomorphism invariance are included in gravity theories. Implications for the Standard-Model Extension are summarized, including recent results showing how the Standard-Model Extension can be modified to accommodate such fixed nondynamical backgrounds.

The bumblebee gravity model includes a class of vector-tensor theories of gravitation where the vector field couples to the Ricci tensor quadratically. We obtain an analytical spherical black-hole solution in this model. The solution has four parameters, expanding the two-parameter solution family known in the literature. Special choices of the parameters are pointed out and discussed.

Lorentz-violating Yukawa couplings lying within the renormalizable part of the SME generate Lorentz-invariant one-loop contributions to electromagnetic moments of fermions. This note provides a discussion of such contributions and presents bounds on SME coefficients from experimental data on electromagnetic moments. Constraints as restrictive as ∼ 10⁻¹⁴ are found.

Symmetric teleparallel gravity is an alternative description of the gravitational field as an effect of nonmetricity rather than curvature of spacetime. For a specific choice of the symmetric teleparallel Lagrangian, the symmetric teleparallel gravity dynamics is equivalent to General Relativity (GR), and it is called the symmetric teleparallel equivalent to General Relativity. We propose local Lorentz-violating dynamics in the gravitational sector of this framework. Lorentz violation is trigged by the vacuum expectation value of the well-known bumblebee field, whose vacuum expectation value couples to the nonmetricity tensor. The effects of such couplings on the cosmological evolution are investigated.

A straightforward method to compute Hamilton’s density for theories that are linear in spacetime curvature is provided. It is shown that the lapse function and shift vector still give rise to primary constraints, while the induced metric gives rise to nontrivial evolution equations. The corresponding Hamilton’s density can always be obtained, albeit in a formal sense.

This article summarizes an investigation of the connection between the hadron-level scalar effective-field-theory treatment of Lorentz-symmetry violation in neutral-meson oscillations and the corresponding quark-level d = 5 nonminimal SME approach. The correspondence between the quark-level a⁽⁵⁾ term is identified to first order in CPT violation based on the expectation that C, P, and T symmetries and the spontaneously broken chiral symmetry of QCD should hold for both formalisms. These can be related to the phenomenological parameter describing possible CPT violation in meson oscillations. A general result facilitating searches for kaons is given.

The AEḡIS collaboration is underway to directly measure the gravitational free-fall of neutral antimatter atoms. The experiment recently succeded in producing a pulsed cold antihydrogen source for the first time, and has now entered into its second phase, which aims at the formation of a slow antihydrogen beam and subseuqently a first proof-of-concept gravitational measurement. Major upgrades have been made, such as an improved antihydrogen production scheme and a new state-of-the-art antiproton trap. AEḡIS was also connected to CERN’s new antiproton deceleration facility ELENA and achieved first antiproton catching in late 2021.

Short-range gravity experiments with striped design of the test and source masses offers uniquely sensitive probes for Lorentz violation. In our previous work, we proposed to combine horizontally and vertically striped experiments to constrain the violating parameters. Here, we further point out that adopting the vertically striped structure with the experimental setup placed at two azimuth angles has more experimental operability. For the experiment, we have completed the assembly and measurement of the torsion pendulum.

The evolution of squeezed coherent states of motion for trapped ions is investigated by applying the time-dependent variational principle for the Schrödinger equation. The method is applied in case of Paul and combined traps, for which the classical Hamiltonian and equations of motion are derived. Hence, coherent states provide a natural framework to: (a) engineer quantum correlated states for trapped ions intended for ultraprecise measurements, (b) explore the mechanisms responsible for decoherence, and (c) investigate the quantum–classical transition.

We discuss three manners to implement Lorentz-symmetry breaking in a superfield theory formulated within the superfield formalism, that is, deformation of the supersymmetry algebra, introducing an extra superfield whose components can depend on Lorentz-violating vectors (tensors), and adding new terms proportional to Lorentz-violating vectors (tensors) to the superfield action. We illustrate these methodologies with examples of quantum calculations.

Adopting a non-relativistic reduction method, we study the one-fermion matrix elements between the fermion–gravity and the fermion–photon interactions in the presence of minimal Lorentz-violating fermion coefficients. We prescribe the Lense–Thirring metric with the test-particle assumption, as this metric is essentially curved and may demonstrate some novel Lorentz-violating matter–gravity couplings beyond the conventional tests of the equivalence principle. With some bold but reasonable assumptions, we get a Lorentz-violating spin–gravity interaction Hamiltonian, from which we derive Lorentz-violating corrections to spin precession and gravitational acceleration. With some ad hoc assumptions, we get some very rough bounds on several Lorentz-violating coefficients, such as $|3\overrightarrow{\tilde{H}}-2\overrightarrow{b}|\le 1.46\times {10}^{-5}\text{eV}$, from spin–gravity measurements like those with Gravity Probe B.

The Hamiltonian formulation of the gravitational sector of the Standard-Model Extension with nondynamical fields u and s^μν is studied. We provide the relevant Hamiltonians that describe the constrained phase space and the dynamics of the induced metric on the ADM hypersurface. The generalization of the Gibbons–Hawking–York boundary term has been crucial to prevent second time derivatives of the metric tensor in the Hamiltonians. By extracting the dynamics and constraints from the Einstein equations we have proved the equivalence between the Lagrangian and Hamiltonian formulations.

The IceCube collaboration has set stringent limits on neutrino-sector isotropic SME coefficients through the measurement of astrophysical neutrino-flavor data. We investigate the consequences of these limits on various new physics models.

We discuss the idea of Lorentz violation with dynamical torsion and show that more stringent bounds on torsion can be found if we assume massive torsion and from CERN’s LEP2 experimental data. From massive torsion, bounds of 10⁻³⁸ GeV may be obtained.

We look for modifications that can be derived from the Maxwell sector of the SME for the interaction between electrical charges and the electromagnetic field. The kind of problem that we are looking into is the one that might be found in a standard textbook on electromagnetism: given a set of electrical charges, in the presence of some non-trivial boundary condition (such as a mirror), find the electromagnetic field and the interaction energy between those charges. To study such a kind of problem in the presence of LV coefficients, we calculate the modified propagator for the Maxwell field, and use it to calculate the energy of a system given by a semi-transparent mirror and a point-like charge. We show how new effects appear in this case, such as a spontaneous torque acting on the system.

An overview of recent progress on searches for Lorentz- and CPT-violating signals with confined particles and antiparticles in Penning traps is presented. In the context of the Standard-Model Extension, leading-order shifts in the cyclotron and anomaly frequencies of a confined particle and antiparticle due to Lorentz and CPT violation are provided. The two frequencies are then related to comparisons of charge-to-mass ratios and magnetic moments between particles and antiparticles. Applying reported results from Penning-trap experiments leads to new limits on various coefficients for Lorentz violation.

The Standard-Model Extension is a framework that catalogs all Lorentz-violating field operators. We investigate the anisotropic correction to the Newtonian gravitational energy for spheroids in the minimal gravitational Standard-Model Extension and solve the rotation dynamics of spheroids. The forced-precession solution given by Nordtvedt in the parametrized post-Newtonian formalism is recovered and applied to constrain the coefficients for Lorentz violation with two solitary millisecond pulsars. The other solution describes an otherwise freely precessing star in the presence of Lorentz violation. The observational consequences on radio signals and continuous gravitational waves emitted by neutron stars are studied.

We investigate the possible degeneracy between the two scenarios, Lorentz violation and non-standard interactions, in the context of mass-induced neutrino oscillation. For current and upcoming fixed-baseline experiments, it is practically impossible to distinguish between these two scenarios. Here, we show how the core-passing atmospheric neutrinos can break this degeneracy. Using the Iron Calorimeter detector simulations at the India-based Neutrino Observatory, we demonstrate that such a distinction is indeed possible.

The swampland conjectures from string theory have had very interesting implications for cosmology and particularly for Inflation. It has been shown that the single-field inflationary models in a GR-based cosmology are in unavoidable tensions with these conjectures and so it becomes interesting to see whether there is a way to overcome the issues of the swampland and single-field inflation in an essentially GR-based cosmology. We show that this can be the case if one considers a certain type of Lorentz-violating inflationary scenario. We work out the requirements for these inflationary models to be swampland consistent and then show how this scenario allows some popular inflationary potentials to be swampland consistent as well.

Muon g-2 data can be used to study sidereal variations in the anomalous muon precession rate, which is one of the important signatures of CPT- and Lorentz-invariance violation. The discussion in this work will focus on the framework that has been used to study sidereal variations in the anomalous muon precession rate in Muon g-2 Run 2 data. Also, a brief introduction will be given about the blinding framework that will be used on Run 2/3 data of the Muon g-2 experiment. This blinding framework will keep the actual result of the experiment masked from the analyzer during the analysis process.

We report on the latest results on quantum-coherence and CPT-symmetry tests from 1.7 fb⁻¹ integrated luminosity collected at the Frascati ϕ-factory DAΦNE. A data sample of 1.7 × 10⁹ decays in the K_SK_L → π⁺π⁻π⁺π⁻ channel allows for precision tests of destructive quantum interference preventing entangled kaon decay at the same proper time difference Δt from production. We reconstruct decoherence and CPT-violation parameters from several phenomenological models with improved accuracy and inference techniques from previous analyses. We find no evidence of new physics and set the most stringent limits on such models to date. For some parameters we reach sensitivity to the quantum-gravity scale.

We present some preliminary results of our study of quantum-gravitational decoherence in a three-neutrino framework. In this context, we discuss the implications of diagonal and non-diagonal decoherence matrices for Dirac and Majorana neutrinos for CPT violation. We find that different choices for the decoherence matrices may lead either to CPT violation or conservation.

In what follows, we will briefly describe how to build a field theory of a complex scalar field in κ-Minkowski spacetime. After introducing the action, we will shortly describe its properties under both continuous and deformed symmetry transformations. We will then describe how to compute the charges and describe their non-trivial properties due to κ-deformation. We will conclude with the experimental significance of the model, particularly in the context of decay-probability differences between particles and antiparticles.

The Deep Underground Neutrino Experiment is a next-generation long-baseline neutrino-oscillation experiment that will start operating in a few years and will conduct a wide range of searches for physics beyond the Standard Model. In this work we investigate the neutrino sector of the Standard-Model Extension considering two coefficients. We modify the General Long Baseline Experiment Simulator to compute the expected number of events and perform a minimum square analysis to determine the best-fit values and allowed ranges of the coefficients for several confidence levels. We compare our results with previous calculations made at the probability level.

Lorentz invariance plays a fundamental role in modern physics. However, tiny violations of Lorentz invariance may arise in some candidate quantum-gravity theories. Using a total of 50 events in the gravitational-wave transient catalogs GWTC-1 and GWTC-2, we perform an analysis of the anisotropic birefringence phenomenon in gravitational waves. The use of multiple events allows us to completely break the degeneracy among gravitational Lorentz-invariance-violation coefficients and globally constrain the coefficient space. Compared to previous results at mass dimensions five and six for the Lorentz-violating operators, we tighten the global limits on 34 coefficients by factors ranging from two to seven.

Possible symmetry-breaking effects during gravitational-wave propagation are investigated using the Standard-Model Extension and the open-source LIGO algorithm library suite. We bridge the gap between the theory of spacetime-symmetry breaking and the analysis of gravitational-waves signals. We analyze directly the LIGO-Virgo-KAGRA interferometers’ strain, bypassing reliance on posterior parameters inferred under a GR model.

J-PET is a photon detector built of plastic scintillators, which already has been commissioned for CPT studies in the decays of positronium. In the first experiment, J-PET has achieved a sensitivity to CPT violation at a level of 10⁻⁴, and now it aims to reach a level of 10⁻⁵. This will be done by enhancing the three-photon registration efficiency for ortho-positronium decays using a new layer of densely packed plastic scintillators termed Modular J-PET. We present the simulation studies performed for different experimental detection setups to be used for the next CPT test with the Modular J-PET detector.

In this work, we deepen the correspondence between Generalized Uncertainty Principles and quantum dynamics on curved momentum space. In particular, we investigate the linear and quadratic Generalized Uncertainty Principle. Similar to earlier work, the resulting curvature tensor in the dual theory is proportional to the coordinate non-commutativity of the original formulation.

We study a CPT-even Lorentz-breaking extension of the scalar QED. We calculate the one-loop contributions in the Lorentz-violating parameters to the two-point functions of the scalar and gauge fields. We find that the two background tensors coming from the two sectors (scalar and gauge) are mixed in the one-loop corrections. This shows that these two Lorentz-breaking terms cannot be studied in an isolated form. Besides, the results in the gauge sector are confirmed to be transversal.

In the framework of Carrol–Field–Jackiw electrodynamics we calculate the spectral distribution of the Cherenkov radiation produced by a charge moving at constant velocity in a chiral medium. We find zero, one, or two Cherenkov angles according to the relation between the velocity of the particle and the refraction index of the medium.

The following section is included:

• Author Index