Lorentz Invariance Research Articles

Inflationary Adler conditions

We derive a new soft theorem that corresponds to the spontaneous breaking of Lorentz boosts. This is motivated by the dynamics of inflation in the sub-horizon (flat-space) limit, where spacetime becomes flat but Lorentz boosts are still broken. In this limit, the scattering amplitudes become sensible observables. We relate the soft emission of a Goldstone boson to the (non-relativistic) Lorentz boost of the hard scattering amplitudes. This is the on-shell avatar of the spontaneous breaking of Lorentz boosts, analogous to the Adler zero of pions in the chiral symmetry breaking. We comment on several applications to inflation, including the demonstration that Dirac-Born-Infeld Inflation is the unique theory that has an emergent Lorentz invariance when the boosts are spontaneously broken.

Three-particle Lellouch-Lüscher formalism in moving frames

A manifestly relativistic-invariant Lellouch-Lüscher formalism for the decays into three identical particles with no two-to-three transitions is proposed. Similarly to [1], the formalism is based on the use of the non-relativistic effective Lagrangians. Manifest Lorentz invariance is guaranteed, as in [2], by choosing the quantization axis along the total four-momentum of the three-particle system. A systematic inclusion of the higher-order derivative couplings, as well as higher partial waves is addressed.

Lorentz invariance violation induced threshold anomaly versus very-high energy cosmic photon emission from GRB 221009A

It has been reported that the Large High Altitude Air Shower Observatory (LHAASO) observed very high energy photons from GRB 221009A, with the highest energy reaching 18 TeV. We find that observation of such high energy photons is quite nontrivial since extragalactic background light could absorb these photons severely and the flux is too weak to be observed. Therefore we discuss a potential mechanism for us to observe these photons, and suggest that Lorentz invariance violation induced threshold anomaly of the process γγ→e−e+ provides a candidate to explain this phenomenon.

On the algebraic approach to GUP in anisotropic space

Motivated by current searches for signals of Lorentz symmetry violation in nature and recent investigations on generalized uncertainty principle (GUP) models in anisotropic space, in this paper we identify GUP models satisfying two criteria: (i) invariance of commutators under canonical transformations, and (ii) physical independence of position and momentum on the ordering of auxiliary operators in their definitions. Compliance of these criteria is fundamental if one wishes to unambiguously describe GUP using an algebraic approach and, surprisingly, neither is trivially satisfied when GUP is assumed within anisotropic space. As a consequence, we use these criteria to place important restrictions on what or how GUP models may be approached algebraically.

Three- and four-point functions in CPT -even Lorentz-violating scalar QED

The renormalization of quantum field theories usually assumes Lorentz and gauge symmetries, besides the general restrictions imposed by unitarity and causality. However, the set of renormalizable theories can be enlarged by relaxing some of these assumptions. In this work, we consider the particular case of a CPT-preserving but Lorentz-breaking extension of scalar QED. For this theory, we calculate the one-loop radiative corrections to the three- and four-point scalar-vector vertex functions, at the lowest order in the Lorentz violation parameters; and we explicitly verify that the resulting low-energy effective action is compatible with the usual gauge invariance requirements. With these results, we complete the one-loop renormalization of the model at the leading order in the Lorentz-violating parameters.

Three-point energy correlators and the celestial block expansion

We study the three-point energy correlator (EEEC), defined as a matrix element of a product of three energy detectors at different locations on the celestial sphere. Lorentz symmetry implies that the EEEC can be decomposed into special functions called celestial blocks. We compute three-point celestial blocks in an expansion around the collinear limit, where the three detectors approach each other on the celestial sphere. The leading term is a traditional d – 2-dimensional four-point conformal block, and thus the collinear EEEC behaves like a conformally-invariant four-point function in d – 2 dimensions. We obtain the coefficients of the conformal block decomposition for the collinear EEEC at leading nontrivial order in weakly-coupled \U0001d4a9 = 4 SYM and QCD. These data allow us to make certain all-orders predictions for the collinear EEEC in various kinematic limits, including the OPE limit and the double lightcone limit. We also study Ward identities satisfied by the EEEC and compute contact terms in the EEEC in weakly-coupled \U0001d4a9 = 4 SYM. Finally, we study the celestial block expansion of the EEEC in planar \U0001d4a9 = 4 SYM at strong coupling, determining celestial block coefficients to leading and first subleading order at large λ.

Observation of highly anisotropic bulk dispersion and spin-polarized topological surface states in CoTe2

We present CoTe2 as a new type-II Dirac semimetal supporting Lorentz symmetry violating Dirac fermions in the vicinity of the Fermi energy. By combining first principle ab-initio calculations with experimental angle-resolved photo-emission spectroscopy results, we show the CoTe2 hosts a pair of type-II Dirac fermions around 90 meV above the Fermi energy. In addition to the bulk Dirac fermions, we find several topological band inversions in bulk CoTe2, which gives rise to a ladder of spin-polarized surface states over a wide range of energies. In contrast to the surface states which typically display Rashba-type in-plane spin splitting, we find that CoTe2 hosts novel out-of-plane spin polarization as well. Our work establishes CoTe2 as a potential candidate for the exploration of Dirac fermiology and applications in spintronic devices, infrared plasmonics, and ultrafast optoelectronics.

Generalised uncertainty relations from finite-accuracy measurements

In this short note we show how the Generalised Uncertainty Principle (GUP) and the Extended Uncertainty Principle (EUP), two of the most common generalised uncertainty relations proposed in the quantum gravity literature, can be derived within the context of canonical quantum theory, without the need for modified commutation relations. A generalised uncertainty principle-type relation naturally emerges when the standard position operator is replaced by an appropriate Positive Operator Valued Measure (POVM), representing a finite-accuracy measurement that localises the quantum wave packet to within a spatial regionσg> 0. This length scale is the standard deviation of the envelope function,g, that defines the positive operator valued measure elements. Similarly, an extended uncertainty principle-type relation emerges when the standard momentum operator is replaced by a positive operator valued measure that localises the wave packet to within a regionσ̃g>0in momentum space. The usual generalised uncertainty principle and extended uncertainty principle are recovered by settingσg≃ℏG/c3, the Planck length, andσ̃g≃ℏΛ/3, where Λ is the cosmological constant. Crucially, the canonical Hamiltonian and commutation relations, and, hence, the canonical Schrödinger and Heisenberg equations, remain unchanged. This demonstrates that generalised uncertainty principle and extended uncertainty principle phenomenology can be obtained without modified commutators, which are known to lead to various pathologies, including violation of the equivalence principle, violation of Lorentz invariance in the relativistic limit, the reference frame-dependence of the “minimum” length, and the so-called soccer ball problem for multi-particle states.

Erratum to “The Asymmetry of the Cosmic Microwave Background Radiation as Signature of Local Lorentz Invariance Violation”

Erratum to “The Asymmetry of the Cosmic Microwave Background Radiation as Signature of Local Lorentz Invariance Violation”

Null boundary gravitational charges from local Lorentz symmetries

In this paper, we revisit the null boundary gravitational charge in the Newman-Penrose formalism with special emphasis on the charges from local Lorentz transformations. We find that there is one more charge derived from the local Lorentz transformation and the new charge is purely from the Holst term. This reveals a remarkable fact that trivial terms which do not change classical equations of motion can not only affect the boundary degrees of freedom through their contributions to the boundary charges but also have their own rights to create new boundary degrees of freedom.

Development of a Compton telescope calorimeter module for MeV-range gamma-ray astronomy

Gamma-ray astronomy in the MeV energy range shows a lack of sensitivity compared to other gamma-ray energy bands. Several space observatory projects are proposed to space agencies to fill this gap. The COMCUBE CubeSat project will focus on the measurement of the polarization of the prompt emission of gamma-ray bursts (GRBs) which can provide an understanding of the physics of ultra-relativistic jets. Furthermore, the linear polarization of distant gamma-ray sources could be a probe to study the fundamental physics related to the Lorentz invariance violation. A Compton telescope is particularly well-suited for that purpose. We develop an instrument including double-sided silicon strip detectors and scintillation crystals coupled to a pixelated photodetector. The incoming photon undergoes an inelastic scattering in one or several layers of a position-sensitive silicon strip detector before being absorbed in a position-sensitive calorimeter based on inorganic scintillators. The measurement of both positions and energy deposits enables the determination of the photon’s source direction. It also enables measurement of the linear polarization of the incident gamma-rays. In this contribution, we present the results of the extensive work we have carried out to develop the calorimeter and its integration into a Compton telescope prototype. We conclude by showing the first image and polarization measurements.

Constraining higher-spin S-matrices

There are various no-go theorems that tightly constrain the existence of local higher-spin theories with non-trivial S-matrix in flat space. Due to the existence of higher-spin Yang-Mills theory with non-trivial scattering amplitudes, it makes sense to revisit Weinberg’s soft theorem — a direct consequence of the Lorentz invariance of the S-matrix that does not take advantage of unitarity and parity invariance. By working with the chiral representation — a representation originated from twistor theory, we show that Weinberg’s soft theorem can be evaded and non-trivial higher-spin S-matrix is possible. In particular, we show that Weinberg’s soft theorem is more closely related to the number of derivatives in the interactions rather than spins. We also observe that all constraints imposed by gauge invariance of the S-matrix are accompanied by polynomials in the soft momentum of the emitted particle where the zeroth order in the soft momentum is a charge conservation law.

Noncommutative Yang model and its generalizations

Long time ago, Yang [Phys. Rev. 72, 874 (1947)] proposed a model of noncommutative spacetime that generalized the Snyder model to a curved background. In this paper, we review his proposal and the generalizations that have been suggested during the years. In particular, we discuss the most general algebras that contain as subalgebras both de Sitter and Snyder algebras, preserving Lorentz invariance, and are generated by a two-parameter deformation of the canonical Heisenberg algebra. We also define their realizations on quantum phase space, giving explicit examples, both exact and in terms of a perturbative expansion in deformation parameters.

Decay of superluminal neutrinos in the collinear approximation

The kinematics of the three-body decay, with a modified energy-momentum relation of the particles due to a violation of Lorentz invariance, is presented in detail in the collinear approximation. The results are applied to the decay of superluminal neutrinos producing an electron-positron or a neutrino-antineutrino pair. Explicit expressions for the energy distributions, required for a study of the cascade of neutrinos produced in the propagation of superluminal neutrinos, are derived.

Grimoire1 of the MAGIC telescopes

The MAGIC (Major Atmospheric Gamma-ray Imaging Cherenkov) telescopes are a system of two Cherenkov telescopes located on the Canary island of La Palma (Spain), at the Roque de Los Muchachos Observatory, and operating in stereo mode since 2009. Their design and dedicated trigger system allows to reach an energy threshold of 50 GeV, which can be lowered to 15 GeV when using the Sum-Trigger-II. This made it possible to observe sources at the limit of detection for imaging atmospheric Cherenkov telescopes (z∼1) and to deeply study the Geminga pulsar tail emission. A strategy of alert follow-ups from other facilities and the fast repositioning of the telescopes made possible the detection of the first neutrino associated with a blazar and of gamma-ray bursts in the very-high-energy (VHE, E>100 GeV) gamma-ray band, respectively. Moreover, the discovery of GRB190114C allowed a test of general relativity through the study of the Lorentz Invariant Violation. Recently MAGIC observed the first VHE gamma-ray nova, RS Ophiuchi, revealing that protons are accelerated to hundreds of gigaelectronvolts in the nova shock. In this talk we will go through the MAGIC recent highlights in the study of galactic and extragalactic sources, spanning from multimessenger astronomy to astroparticle and fundamental physics.

Hulthén potential under the Lorentz symmetry violation effects due to the coupling between the vector field f μ γ 5and the derivative of the fermionic field

We search for Lorentz symmetry violation effects caused by the coupling between a fixed vector field and the derivative of the fermionic field in the nonrelativistic regime. By working with dimensions, we study nonrelativistic effects of the Lorentz symmetry violation on the energy eigenvalues of the Hulthén potential and the deformed Hulthén potential.

Geometric Event-Based Quantum Mechanics

We propose a special relativistic framework for quantum mechanics. It is based on introducing a Hilbert space for events. Events are taken as primitive notions (as customary in relativity), whereas quantum systems (e.g. fields and particles) are emergent in the form of joint probability amplitudes for position and time of events. Textbook relativistic quantum mechanics and quantum field theory can be recovered by dividing the event Hilbert spaces into space and time (a foliation) and then conditioning the event states onto the time part. Our theory satisfies the full Lorentz symmetry as a ‘geometric’ unitary transformation, and possesses relativistic observables for space (location of an event) and time (position in time of an event).

Conserved currents for the gauge-field theory with Lorentz symmetry group and a composite theory of gravity

For the Yang-Mills–type gauge-field theory with Lorentz symmetry group, we propose and verify an explicit expression for the conserved currents in terms of the energy-momentum tensor. A crucial ingredient is the assumption that the gauge symmetry arises from the decomposition of a metric in terms of tetrad variables. The currents exist under the weak condition that the energy-momentum tensor and the Ricci tensor commute. We show how the conserved currents can be used to obtain a composite theory of gravity and discuss the static isotropic field around a point mass at rest.

Violation of Lorentz symmetries and thermal effects in Compton scattering

In this paper, the differential cross section for the Compton scattering process is calculated. Two types of corrections are investigated: corrections due to violation of Lorentz symmetry and thermal effects. An extended QED is considered to introduce the parameter that leads to the breaking of symmetry. While temperature effects are introduced using the Thermofield Dynamics formalism. It is shown that the differential cross section changes with both corrections. These corrections are dominant at appropriate limits. These special cases are analyzed and compared with other results from the literature.

Logarithmic catastrophes and Stokes’s phenomenon in waves at horizons

Waves propagating near an event horizon display interesting features including logarithmic phase singularities and caustics. We consider an acoustic horizon in a flowing Bose–Einstein condensate where the elementary excitations obey the Bogoliubov dispersion relation. In the Hamiltonian ray theory the solutions undergo a broken pitchfork bifurcation near the horizon and one might therefore expect the associated wave structure to be given by a Pearcey function, this being the universal wave function that dresses catastrophes with two control parameters. However, the wave function is in fact an Airy-type function supplemented by a logarithmic phase term, a novel type of wave catastrophe. Similar wave functions arise in aeroacoustic flows from jet engines, path integrals in radio astronomy, and also gravitational horizons if dispersion which violates Lorentz symmetry in the UV is included. The approach we take differs from most previous authors in that we analyze the behavior of the integral representation of the wave function using exponential coordinates. This allows for a different treatment of the branch cuts and gives rise to an analysis based purely on saddlepoint expansions. We are thereby able to resolve the multiple real and complex waves that interact at the horizon and its companion caustic. We find that the horizon is a physical manifestation of a Stokes surface, marking the place where a wave is born, and that the horizon and the caustic do not in general coincide: the finite spatial region between them delineates a broadened horizon.