Lorentz Invariance Research Articles

Symmetric vs. chiral approaches to massive fields with spin

Abstract Massive higher spin fields are notoriously difficult to introduce interactions when they are described by symmetric (spin)-tensors. An alternative approach is to use chiral description that does not have unphysical longitudinal modes. For low spin fields we show that chiral and symmetric approaches can be related via a family of invertible change of variables (equivalent to parent actions), which should facilitate introduction of consistent interactions in the symmetric approach and help to control parity in the chiral one. We consider some examples of electromagnetic and gravitational interactions and their transmutations when going to the chiral formulation. An interesting feature of the relation is how second class constraints get eliminated while preserving Lorentz invariance.

Weak field deflection angle and analytical parameter estimation of the Lorentz-violating Bumblebee parameter through the black hole shadow using EHT data

Abstract We explored how the Lorentz symmetry breaking parameter $\ell$ affects the Reissner-Nordst"{o}m BH solution in the context of weak field deflection angle, and the black hole shadow. We aim to derive the general expression for the weak deflection angle using the non-asymptotic version of the Gauss-Bonnet theorem, and we presented a way to simplify the calculations under the assumption that the distance of the source and the receiver are the same. \textcolor{blue}{Through the Solar System test, $\ell$ is constrained from around $-10^{-9}$ orders of magnitude to $0$, implying challenging detection of $\ell$ through the deflection of light rays from the Sun.} We also studied the black hole shadow in an analytic way, where we applied the EHT results under the far approximation in obtaining an estimate expression for $\ell$. Using the realistic values of the black hole mass and observer distance for Sgr. A* and M87*, it was shown that $M/r_{\rm o} \neq 1$ is satisfied, implying the relevance and potential promise of the spontaneous Lorentz symmetry breaking parameter's role on the shadow radius uncertainties as measured by the EHT. We find constraints for $\ell$ to be negatively valued, where the upper and lower bounds are $\sim -1.94$ and $\sim -2.04$, respectively.

Constraint of d = 8 Lorentz Invariance Violation with New Experimental Design

Short-range gravity experiments are more suitable for the testing of high-order Lorentz symmetry breaking effects. In our previous work, we proposed a new experimental design based on precision torsion balance technology to test the Lorentz violation force effect that varies inversely with the fourth power of distance (corresponding to mass dimension d = 6 term), and the corresponding experiment is currently underway. In this paper, we focus on analyzing the potential of this experimental scheme to test the Lorentz violation force that varies inversely with the sixth power of distance (corresponding to mass dimension d = 8 term). The results show that, compared with the current best limit, the new experimental scheme can improve the constraints on the Lorentz violation coefficients with d = 8 by at least one order of magnitude.

Topological signatures of triply degenerate fermions in Heusler alloys: an ab initio study

Triply degenerate nodal point (TP) fermions, lacking elementary particle counterparts, have been theoretically anticipated as quasiparticle excitations near specific band crossing points constrained by distinct space-group symmetries instead of Lorentz invariance. Here, based onfirst-principlescalculations and symmetry analysis, we demonstrate the presence of TP fermions in Heusler alloys. Furthermore, we predict that these Heusler alloys are dynamically stable, exhibiting TP fermions along four distinctC3axes in the F-43m space group. We show thatα-LiCaPdSb harbours peculiar Fermi arcs and surface states on the (111) and (001) crystal facets, owing to the coexistence of threefold rotational and time reversal symmetry. More interestingly, a modest tensile strain can increase the distance of fermions along the Γ-Lhigh symmetric line by as much as 21.10%, which give rise to measurable Fermi arcs. Furthermore, we investigate non-trivial topological insulator phase inβ-LiCaPdSb, by changing the chemical environment through placing transition metal atoms at various Wyckoff positions. Theβ-LiCaPdSb harbour a semi-metallic nature, and by breaking cubic symmetry, it undergoes a transition from semi-metal to a non-trivial topological insulator. In addition, for the first time, rare-earth LaPtBi half-Heusler alloy is examined under strain to uncover multiple band inversions associated with the TP fermionic phase. The observed multiple band inversion is entirely unaffected by spin-orbit coupling. We show that the LaPtBi compound hosts TP fermions, which are linked to aZ2topological invariant. Remarkably, with clear band crossings and multiple band inversion, we point out the possibilities of the LaPtBi for displaying a rich topological phase diagram. Our work provides a prototype material platform for experimental detection through angle-resolved photoemission spectroscopy or scanning tunnelling spectroscopy and practical spintronic applications.

Accretion of Vlasov gas onto a black hole in the Kalb–Ramond field

Abstract We investigate the accretion of Vlasov gas onto a static, spherically symmetric black hole (BH) influenced by the Kalb–Ramond (KR) field, focusing on the effects of Lorentz symmetry breaking (LSB) parameters. We employ the Maxwell–Jüttner distribution to model the gas at infinity and derive key quantities such as the particle current density and mass accretion rate. Our findings reveal that an increase in the LSB parameter results in a decrease in the mass accretion rate. We also present explicit formulations of the accretion rate in the high-temperature limit and find the result is quite different from the result in Bumblebee model.

Vacuum energy density for interacting real and complex scalar fields in a Lorentz symmetry violation scenario

Vacuum energy density for interacting real and complex scalar fields in a Lorentz symmetry violation scenario

Direct Evidence for Preburst Stage of Gamma-Ray Burst from GRB 221009A Data

Previous research on Lorentz invariance violation in photons from gamma-ray bursts (GRBs) suggested a scenario where multi-GeV photons could be emitted before lower-energy photons at the GRB source frame. This implies the existence of a new preburst phase in addition to the traditionally identified prompt and afterglow stages observed in earlier studies. In this study, we present direct evidence for this novel preburst phase in GRBs based on recent observations of GRB 221009A. Our analysis leverages data from the Fermi Gamma-ray Burst Monitor and Large Area Telescope detectors of the Fermi Gamma-ray Space Telescope, as well as data from the KM2A detector of the Large High Altitude Air-shower Observatory.

Fermionic Casimir energy in Horava–Lifshitz scenario

In this work, we investigate the violation of Lorentz symmetry through the Casimir effect, one of the most intriguing phenomena in modern physics. The Casimir effect, which represents a macroscopic quantum force between two neutral conducting surfaces, is widely regarded as a triumph of Quantum Field Theory. In this study, we present new results for the Casimir effect, focusing on the contribution of mass associated with fermionic quantum fields confined between two large parallel plates, in the context of Lorentz symmetry violation within the Horava–Lifshitz formalism. To calculate the Casimir energy and pressure, we impose a MIT bag boundary condition on the two plates, compatible with the higher-order derivative term in the modified Dirac equation. Our results reveal a strong influence of Lorentz violation on the Casimir effect. We observe that the Casimir energy is significantly affected, both in intensity and sign, potentially resulting in a repulsive or attractive force between the plates, depending on the critical exponent associated with the Horava–Lifshitz formalism.

Lorentz invariants in particle-wave mechanical systems

In these notes we detail a number of new results involving the Lorentz invariants associated with the special relativistic extension of Newton’s second law proposed in [10] and not included in that text. We first summarise existing results for the two Lorentz invariants ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document} and η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta $$\\end{document} and the angle θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta $$\\end{document} which is the angle in which Lorentz invariance appears as a translational invariance. We then determine new integral formulae involving these quantities and a new relationship which connects the applied forces with the same invariances. This latter relation turns out to be equivalent to the partial differential equation arising from the invariance of the velocity equation dx/dt=u(x,t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{d}x/\ extrm{d}t = u(x, t)$$\\end{document} under a Lorentz transformation. We then provide some specific examples which confirm the validity of the new relation connecting the applied forces with the invariances.

Derivative four-fermion model, effective action and bumblebee generation

In this paper, we study the one-loop effective potential of a derivative four-fermion model. As a result, an exact bumblebee-like potential is radiatively generated. Afterwards, we generalize our study for a finite temperature case and explicitly demonstrate the possibility of phase transitions allowing for the restoration of the Lorentz symmetry. We also investigate the low-energy effective action, from which we obtain the usual kinetic term and the corresponding bumblebee potential.

Mass ladder operators and quasinormal modes of the static BTZ-like black hole in the Einstein-bumblebee gravity

Abstract We investigate the mass ladder operators for the static BTZ-like black hole in the Einstein-bumblebee gravity, and probe the quasinormal frequencies of the mapped modes by the mass ladder operators for a scalar perturbation under the Dirichlet and Neumann boundary conditions. It is found that the mass ladder operators depend on the Lorentz symmetry breaking parameter, and the imaginary parts of the frequencies shifted by the mass ladder operators increase with the increase of the Lorentz symmetry breaking parameter under two boundary conditions. It should be noted that, under the Neumann boundary condition, the mapped modes caused by the mass ladder operator $D_{0,k_+}$ are unstable. Moreover, the mass ladder operators do not change the Breitenlohner-Freedman bound for the scalar modes, just as in the usual BTZ black hole. These results could help us to further understand the conformal symmetry and Lorentz symmetry breaking in the Einstein-bumblebee gravity.

Doubly special relativity as a nonlocal quantum field theory

In this work, we explore the quantum theories of the free massive scalar, the massive fermionic, and the electromagnetic fields in a doubly special relativity scenario. This construction is based on a geometrical interpretation of the kinematics of this kind of theory. In order to describe the modified actions, we find that a higher (indeed infinite) derivative field theory is needed, from which the deformed kinematics can be read. From our construction, we are able to restrict the possible models of doubly special relativity to those that preserve linear Lorentz invariance. We quantize the theories and also obtain a deformed version of the Maxwell equations. We analyze the electromagnetic vector potential for both an electric pointlike source and magnetic dipole. We observe that the electric and magnetic fields do not diverge at the origin for some models described with an anti–de Sitter momentum space, but they do for a de Sitter space in both problems. Published by the American Physical Society 2024

Lorentz-covariant spinor wave packet

We propose a novel formulation for a manifestly Lorentz-covariant spinor wave-packet basis. The traditional definition of the spinor wave packet is problematic due to its unavoidable mixing with other wave packets under Lorentz transformations. Our approach resolves this inherent mixing issue. The wave packet we develop constitutes a complete set, enabling the expansion of a free spinor field while maintaining Lorentz covariance. Additionally, we present a Lorentz-invariant expression for zero-point energy. Published by the American Physical Society 2024

Fermi acceleration under Lorentz invariance violation

In this paper, the acceleration of particles in astrophysical sources by the Fermi mechanism is revisited under the assumption of Lorentz invariance violation (LIV). We calculate the energy spectrum and the acceleration time of particles leaving the source as a function of the energy beyond which the Lorentz invariance violation becomes relevant. Lorentz invariance violation causes significant changes in the acceleration of particles by the first and second-order Fermi mechanisms. The energy spectrum of particles accelerated by first-order Fermi mechanism under LIV assumption shows a strong suppression for energies above the break. The calculations presented here complete the scenario for LIV searches with astroparticles by showing, for the first time, how the benchmark acceleration mechanisms (Fermi) are modified under LIV assumption.

Interactions in the IKKT matrix model on covariant quantum spacetime

We study the interactions of the higher-spin gauge theory arising from the IKKT matrix model on a covariant quantum FLRW quantum space-time MJ1,3, denoted as HS-IKKT. In particular, we elaborate some of the vertices and observe that they are not manifestly Lorentz invariant in the unitary formulation. We argue that Lorentz invariance of HS-IKKT can be recovered since Lorentz transformations are part of the gauge invariance in the covariant formulation. This statement is verified for some vertices with lowest number of derivatives. The lowest-derivative sector of this theory is expected to be governed by an “almost”-Lorentz-invariant Yang-Mills theory coupled to emergent gravity.

Non-hermitian Dirac theory from Lindbladian dynamics

This study investigates the intricate relationship between dissipative processes of open quantum systems and the non-Hermitian quantum field theory of relativistic fermionic systems. By examining the influence of dissipative effects on Dirac fermions via Lindblad formalism, we elucidate the effects of coupling relativistic Dirac particles with the environment and show the lack of manifest Lorentz invariance. Employing rigorous theoretical analysis, we generalize the collisionless Boltzmann equations for the relativistic dissipation-driven fermionic system and find the Lyapunov equation, which governs the stationary solutions. Using our formalism, one presents a simple non-Hermitian model that the relativistic fermionic particles and anti-particles are stable. Going further, using the solution to the Lyapunov equations, one analyses the effect of dissipation on the stationary charge imbalance of this non-Hermitian model and finds that the dissipation can induce a new kind of charge imbalance compared with the collisionless equilibrium case.

Gravitational lensing and shadow by a Schwarzschild-like black hole in metric-affine bumblebee gravity

In this paper, we investigate the gravitational lensing effect and the shadow around a Schwarzschild-like black hole in metric-affine bumblebee gravity, which leads to the Lorentz symmetry breaking. We first present a generalized formalism for calculating higher-order corrections to light weak bending angle in a static, spherically symmetric and not asymptotically flat spacetime, and then applying this general formalism to the metric-affine bumblebee gravity. Moreover, we derive the light deflection angle and the size of the Einstein ring within the weak field in this scenario. In addition, we analyze the black hole shadow in this theory framework. By using observational data from the Einstein’s ring of the galaxy ESO325-G004 and the black hole shadow of the M87\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{M}87$$\\end{document} galaxy, we estimate the upper bounds of the Lorentz symmetry breaking coefficient ℓ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell $$\\end{document}, respectively.

Holographic Lifshitz flows

Without Lorentz symmetry, generic fixed points of the renormalization group (RG) are labelled by their dynamical (or ‘Lifshitz’) exponent z. Hence, a rich variety of possible RG flows arises. The first example is already given by the standard non-relativistic limit, which can be viewed as the flow from a z = 1 UV fixed point to a z = 2 IR fixed point. In strongly coupled theories, there are good arguments suggesting that Lorentz invariance can emerge dynamically in the IR from a Lorentz violating UV. In this work, we perform a generic study of fixed points and the possible RG flows among them in a minimal bottom-up holographic model without Lorentz invariance, aiming to shed light on the possible options and the related phenomenology. We find: i) A minor generalization of previous models involving a massive vector field with allowed self-couplings leads to a much more efficient emergence of Lorentz invariance than in the previous attempts. Moreover, we find that generically the larger is the UV dynamical exponent zUV the faster is the recovery of Lorentz symmetry in the IR. ii) We construct explicitly a holographic model with a line of fixed points, realizing different Lifshitz scaling along the line. iii) We also confirm the monotonicity of a recently proposed a-function along all our Lorentz violating RG flows.

Matter coupled to 3d quantum gravity: one-loop unitarity

Abstract We expect quantum field theories for matter to acquire intricate corrections due to their coupling to quantum fluctuations of the gravitational field. This can be precisely worked out in 3d quantum gravity: after integrating out quantum gravity, matter fields are effectively described as noncommutative quantum field theories, with quantum-deformed Lorentz symmetries. An open question remains: Are such theories unitary or not? On the one hand, since these are effective field theories obtained after integrating out high energy degrees of freedom, we may expect the loss of unitarity. On the other hand, as rigorously defined field theories built with Lorentz symmetries and standing on their own, we naturally expect the conservation of unitarity. In an effort to settle this issue, we explicitly check unitarity for a scalar field at one-loop level in both Euclidean and Lorentzian space-time signatures. We find that unitarity requires adding an extra-term to the propagator of the noncommutative theory, corresponding to a massless mode and given by a representation with vanishing Plancherel measure, thus usually ignored in spinfoam path integrals for quantum gravity. This indicates that the inclusion of matter in spinfoam models, and more generally in quantum gravity, might be more subtle than previously thought.

Disjointness of inertial KMS states and the role of Lorentz symmetry in thermalization

For any local, translation-covariant quantum field theory on Minkowski spacetime, we prove that two distinct states that are invariant under the inertial time evolutions in different inertial reference frames are disjoint, i.e. neither state is a perturbation of the other, if the states are primary, have separating Gelfand–Naimark–Segal (GNS) vectors, and satisfy a timelike cluster property called the mixing property. These conditions are fulfilled by the inertial Kubo–Martin–Schwinger (KMS) states of the free scalar field, thus showing that a state satisfying the KMS condition relative to one inertial frame is far from thermal equilibrium relative to other inertial frames. We review the property of return to equilibrium (RTE) in open quantum systems theory and discuss the implications of disjointness on the asymptotic behavior of detector systems coupled to states of a free massless scalar field. We argue that the coupled system of an Unruh–DeWitt detector moving with constant velocity relative to the field in a KMS state, or an excitation thereof, cannot thermalize under generic conditions. This leads to an illustration of the physical differences between heat baths in inertial systems and the alleged “heat bath” of the Unruh effect. This paper also sketches the construction and RTE property of the quantum dynamical system of an Unruh–DeWitt detector coupled to a massless scalar field in a KMS state relative to the inertial rest frame of the detector.