Lorentz invariance, vacuum energy, and cosmology
F. R. Klinkhamer
这篇文章回顾了最近的工作，一个新的方法来解决宇宙学常数的问题，它从宏观行为的保守相对论微观变量q。首先讨论真空能量密度的静力学，然后讨论宇宙学背景下的动力学。
This contribution reviews recent work on a new approach to the cosmological constant problem, which starts from the macroscopic behavior of a conserved relativistic microscopic variable q. First, the statics of the vacuum energy density is discussed and, then, the dynamics in a cosmological context.
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Spontaneous Violation of Lorentz Invariance and Ultra-High Energy Cosmic Rays
我们提出，由于矢量场的非零真空期望值<$^μ，局部洛伦兹不变性在高能量下自发地被破坏，作为观测到能量高于GZK截止的超高能宇宙射线的可能解释。讨论了宇宙学中洛伦兹不变性自发破缺的某些后果。
On the consistency of Lorentz invariance violation in QED induced by fermions in constant axial-vector background
我们表明，第一次诱导的奇偶性-甚至洛伦兹不变性违反可以明确地计算在物理上合理的和最低限度地打破维正则化计划，适合定制的自发洛伦兹对称性破缺的场论模型。违反量子电动力学的洛伦兹不变性的量子化是严格审查和一致的，无论是光-像宇宙各向异性轴-矢量或时间-像一个，当存在一个裸露的光子质量。
Impact of Lorentz Violation on Cosmology
讨论了洛伦兹破坏对宇宙学的影响。首先，我们证明了洛伦兹破坏对混沌暴胀模型的动力学行为的影响，并给出了一个有趣的特征。其次，我们提出了Lorentz破坏DGP膜模型，其中膜上的Lorentz破坏项加速当前宇宙。我们推测在Lorentz破坏的DGP模型中鬼消失了。
Quantum Gravity, Cosmology, (Liouville) Strings and Lorentz Invariance
我回顾了非临界弦的某些方面，与量子引力的洛伦兹不变性破坏方法有关。我还讨论了如何非临界弦可能提供一个统一的框架，弦宇宙学和量子引力可以一起处理。
Modern tests of Lorentz invariance
受量子引力的启发，在过去的十年里，大量的努力已经投入到测试各种状态下的洛伦兹不变性中。本文综述了洛伦兹不变性测试的理论框架和实验进展，使新的高精度测试成为可能。介绍了目前从地面实验和天体物理观测中对洛仑兹破坏效应的限制。
Diffeomorphism-invariant noncommutative gravity with twisted local Lorentz invariance
本文提出了一种新的非对易时空引力理论，它在一般坐标变换下是不变的，而局部洛伦兹不变性则是通过扭曲的规范对称性来实现的。与现有的非对易引力公式相比，我们的理论要简单得多。
Inspecting absorption in the spectra of extra-galactic gamma-ray sources for insight into Lorentz invariance violation
我们研究了银河系外TeV伽马射线源，如耀变体，在洛伦兹不变性破坏（LIV）的存在下，吸收光谱会是什么样子。对生产与河外背景光修改观察到的光谱，这样的来源，我们表明，违反洛伦兹不变性一般会有一个戏剧性的影响，这种吸收功能。检查这种效应，一个实验性的任务可能在不久的将来实用，可以提供独特的洞察力的可能性LIV。
Theories of gravitation without Lorentz invariance are candidates of low-energy descriptions of quantum gravity. In this review we will describe the phenomenological consequences of the candidates associated to the existence of a preferred time direction
We study renormalization group flows in strongly interacting field theories with fermions that correspond to transitions between a theory without Lorentz invariance at high energies down to a theory with approximate Lorentz symmetry in the infrared. Holographic description of the strong coupling is used. The emphasis is made on emergence of chiral fermions in the low-energy theory.
We explore the interplay of matter with quantum gravity with a preferred frame to highlight that the matter sector cannot be protected from the symmetry-breaking effects in the gravitational sector. Focusing on Abelian gauge fields, we show that quantum gravitational radiative corrections induce Lorentz-invariance-violating couplings for the Abelian gauge field. In particular, we discuss how such a mechanism could result in the possibility to translate observational constraints on Lorentz violation in the matter sector into strong constraints on the Lorentz-violating gravitational couplings.
Lorentz Invariance in Shape Dynamics
形状动力学是正则广义相对论的重构，其中时间重新参数化不变性被“交易”为局部共形不变性。我们探讨了洛伦兹不变性在这个模型中出现在三个方面：作为一个最大的对称性，渐近对称性，和局部不变性。
Spectra of Field Fluctuations in Braneworld Models with Broken Bulk Lorentz Invariance
我们研究了具有破洛伦兹不变性的五维膜世界系统，继续我们以前的论文（arXiv：0712.1136）的发展，其中发现了一族静态自调谐膜世界解，我们证明了几个已知的膜世界模型可以嵌入到这个家族中。在此基础上，我们给出了洛伦兹不变性破缺背景中场涨落谱的定性分析。我们还详细讨论了一个特殊的模型，并研究了它的标量场和旋量场的谱，结果表明，我们所发现的谱具有非常奇特和出乎意料的性质。
Why does the Unruh effect rely on Lorentz invariance, while Hawking radiation does not ?
我们表明，没有洛伦兹不变性，Unruh效应不存在。我们使用修改后的色散关系，并依次描述：非热性质的真空（定义在首选帧）限制的Rindler楔，损失的KMS属性的Wigthman函数，跃迁振幅和跃迁率的均匀加速检测器。这种情况似乎与声学黑洞的霍金辐射形成对比，在某些假设下，它已经被证明对洛伦兹对称性的破坏是鲁棒的。我们解释这种差异。
General relativity with fermions has two independent symmetries: general coordinate invariance and local Lorentz invariance. General coordinate invariance is implemented by the Levi-Civita connection and by Cartan's tetrads both of which have as their action the Einstein-Hilbert action. It is suggested here that local Lorentz invariance is implemented not by a combination of the Levi-Civita connection and Cartan's tetrads known as the spin connection, but by independent Lorentz bosons L_i that gauge the Lorentz group, that couple to fermions like Yang-Mills fields, and that have their own Yang…
Superconducting-gravimeter measurements are used to test the local Lorentz invariance of the gravitational interaction and of matter-gravity couplings. The best laboratory sensitivities to date are achieved via a maximum-reach analysis for 13 Lorentz-violating operators, with some improvements exceeding an order of magnitude.
Testing Lorentz invariance of dark matter
研究了用宇宙学观测约束暗物质偏离洛伦兹不变性的可能性。打破洛伦兹不变性一般引入新的轻引力自由度，我们表示通过一个动态的类时向量场。如果DM不服从洛伦兹不变性，它耦合到这个向量场。我们发现，这种耦合影响的惯性质量的小DM晕不再满足等效原理。对于足够大的DM块，我们确定一个（变色龙）机制，恢复惯性质量，其标准值。因此，引力成团的动力学被修改。两个显著的效应是大尺度结构生长的尺度依赖性增强和DM和重子密度扰动之间的尺度依赖性偏差。与测得的线性物质功率谱的比较，原则上允许绑定偏离洛伦兹不变性的DM在百分比水平。
Violating Lorentz invariance minimally by the emergence of nonmetricity? A Perspective
本文提出应在引力的规范理论框架中理解洛伦兹不变性破坏，指出时空度量-仿射几何的非零非度规性可作为洛伦兹对称性破坏的标志。
Neutrino mixing and Lorentz invariance
我们使用以前的工作希尔伯特空间的混合场导出变形色散关系的中微子味态。然后，我们将讨论如何将这些色散关系纳入框架编码的洛伦兹不变性的故障。我们考虑非线性相对论方案（其中双狭义相对论是一个例子），也允许存在一个首选框架的框架。在这两种情况下，我们都导出了β衰变的谱和终点的表达式，这可以作为中微子经历洛伦兹不变性的特殊方式的实验探针。
The Newton limit of gravity is studied in the presence of Lorentz-violating gravitational operators of arbitrary mass dimension. The linearized modified Einstein equations are obtained and the perturbative solutions are constructed and characterized. We develop a formalism for data analysis in laboratory experiments testing gravity at short range and demonstrate that these tests provide unique sensitivity to deviations from local Lorentz invariance.
We study the consistency of having Lorentz invariance as a low energy approximation within the quantum field theory framework. A model with a scalar and a fermion field is used to show how a Lorentz invariance violating high momentum scale, a physical cutoff rendering the quantum field theory finite, can be made compatible with a suppression of Lorentz invariance violations at low momenta. The fine tuning required to get this suppression and to have a light scalar particle in the spectrum is determined at one loop.
Lorentz Invariance Breakdown and Constraints from Big-Bang Nucleosynthesis
在$^4He$原始丰度的框架下，对Colladay和Kostelecklett提出的标准模型扩展进行了评述。利用目前的观测数据导出了洛伦兹破坏系数的上界。
Two-dimensional Lorentz invariance of spherically symmetric black holes
我们表明，一个静态的球对称黑洞，在一般的引力理论与一般的物质场，具有二维洛伦兹对称性。
Scalar Field for Breaking Lorentz and Diffeomorphism Invariance
一个标量场可以被插入到麦克斯韦和/或爱因斯坦理论中以实现对称性破缺。这种修改的后果进行了讨论。可能的动力学的标量场。
Imperfect fluids, Lorentz violations and Finsler Cosmology
我们构建了一个宇宙学玩具模型的基础上的芬斯勒时空结构。特别是，我们感兴趣的是一个特定的芬斯勒洛伦兹违反理论的基础上弯曲版本的科恩和科恩的非常狭义相对论。对于特定的观察者，芬斯勒流形与黎曼流形的密切导致了相对论宇宙学的极限。一个修正的平坦FRW宇宙学产生。零能量粒子的模拟展现了动力学的一些特殊性质。运动学方程受局部各向异性的影响。洛伦兹违反的种子可能会触发宇宙流体的密度不均匀性。
This brief contribution is devoted to phenomenological consequences of deviations from Lorentz invariance in gravity and dark matter. We will discuss main effects on cosmological observables and current constraints derived from astrophysical and cosmological data.
Lorentz invariance and quantum gravity: an additional fine-tuning problem?
试图将标准的量子场论与引力结合起来，会导致普朗克长度1.6*10^{-35} m附近的通常时空结构的崩溃，并可能违反洛伦兹不变性。对量子引力中优先标架效应的计算进一步激发了对洛伦兹破坏的高精度搜索。在这里，我们解释说，结合已知的基本粒子相互作用与普朗克尺度的首选框架会导致洛伦兹破坏的百分比水平，约20个数量级以上，比以前的估计，除非裸参数的理论是不自然的强烈微调。因此，一个重要的任务不仅是提高精度的搜索违反洛伦兹不变性，但也寻找理论机制，自动保持洛伦兹不变性。
The effects of local Lorentz violation on dispersion and birefringence of gravitational waves are investigated. The covariant dispersion relation for gravitational waves involving gauge-invariant Lorentz-violating operators of arbitrary mass dimension is constructed. The chirp signal from the gravitational-wave event GW150914 is used to place numerous first constraints on gravitational Lorentz violation.
Using a deformed dispersion relation for gravitational waves, Advanced LIGO and Advanced Virgo have been able to place constraints on violations of local Lorentz invariance as well as the mass of the graviton. We summarise the method to obtain the current bounds from the 10 significant binary black hole detections made during the first and second observing runs of the above detectors.
We explore the phenomenon of emergent Lorentz invariance in strongly coupled theories. The strong dynamics is handled using the gauge/gravity correspondence. We analyze how the renormalization group flow towards Lorentz invariance is reflected in the two-point functions of local operators and in the dispersion relations of the bound states. The deviations of these observables from the relativistic form at low energies are found to be power-law suppressed by the ratio of the infrared and ultraviolet scales. We show that in a certain subclass of models the velocities of the light bound states st…
On the use of energy loss mechanisms to constrain Lorentz invariance violations
鉴于最近和可能即将到来的观测非常高的能量天体粒子，如冰立方合作报告，我们重新讨论洛伦兹违反粒子的能量损失机制。我们分析表明，Cohen-Eschhow的能量损失公式与泊松分布的衰变数，其大的波动防止放置的界限洛伦兹不变性违反。然而，该模型忽略了每个过程之后衰减宽度的急剧变化。我们建议用一个考虑到这一点的新分布来取代泊松统计。根据新的统计量，我们研究了平均末态能量及其涨落，并与Cohen-Schnehow的结果进行了对比，讨论了能量损失机制约束违反Lorentz不变性的可靠性.
Hamiltonian Electric/Magnetic Duality and Lorentz Invariance
在（3+1）哈密顿形式下，一般自相互作用规范矢量作用量的电磁不变性的条件和对偶生成元的定义是显而易见的。相反，（3+1）作用量本质上不是洛伦兹不变的。施加狄拉克-施温格应力张量交换子的要求，以执行后者产生一个微分约束的哈密尔顿转化为通常的拉格朗日形式的对偶不变性条件所遵守的麦克斯韦和博恩-因菲尔德理论。我们还讨论了一些类似的标量模型的协方差性质。
A novel structure-preserving algorithm for general relativity in vacuum is derived from a lattice gauge theoretic discretization of the tetradic Palatini action. The resulting model of discrete gravity is demonstrated to preserve local Lorentz invariance and symplectic structure.
On Galilean and Lorentz invariance in pilot-wave dynamics
有人认为，自然的运动学的导频波理论是阿斯特丽德。尽管表面上如此，伽利略不变性并不是低能理论的基本对称性。相反，这是一种人为强加的虚构对称。得出的结论是，寻找一个洛伦兹不变的扩展是物理误导。
One of the disadvantages of the Hamiltonian formulation is that Lorentz invariance is not manifest in the former. Given a Hamiltonian, there is no simple way to check whether it is relativistic or not. One would either have to solve for the equations of motion or calculate the Poisson Brackets of the Noether charges to perform such a check. In this paper we show that, for a class of Hamiltonians, it is possible to check Lorentz invariance directly from the Hamiltonian. Our work is particularly useful for theories where the other methods may not be readily available.
Improved Test of Lorentz Invariance in Electrodynamics
本文报道了低温蓝宝石微波谐振器和氢脉泽的比较结果。实验结果与系统效应的广泛分析一起示出。在此之前，该实验已经对洛仑兹不变性的Alfredy-Thorndike型违反设定了最严格的约束。在这项工作中，我们提出了新的数据和解释我们的结果在一般的洛伦兹违反扩展的标准模型的粒子物理（SME）。在SME的光子部分内，我们的实验对七个SME参数敏感。我们将其中四项的现行限额略为提高，而将另外三项的限额提高7至10倍。
The parity violation at the level of weak interactions and other similar discrete symmetries breaking show that the invariance of laws under the full group of Lorentz transformations can not be taken granted. We examine the principle of Lorentz invariance under the general theory of relativity, and demonstrate the importance of a concept of the spacetime orientation as part of the causal structure of spacetime.
We explore cosmological solutions to Lorentz breaking gravity using the gravitational sector of the Standard Model Extension (SME). By using a simple toy model for Lorentz violation and under the assumption that the so-called $\mathfrak{T}$-tensor is covariantly constant, we show that the gravity sector SME influences basic cosmology. If the approach used in this toy model is valid these results should point the way for more sofisticated studies.
Late-time acceleration and Phantom Divide Line Crossing with Non-minimal Coupling and Lorentz Invariance Violation
我们考虑了两种可供选择的暗能量模型：一种是具有非最小耦合标量场的洛伦兹不变性保持模型，另一种是具有最小耦合标量场的洛伦兹不变性破坏模型。我们研究了在这些情况下状态方程参数的加速膨胀和动力学。虽然最小耦合标量场不具备成为具有宇宙学常数线交叉的暗能量候选者的能力，但具有洛伦兹不变性的非最小耦合标量场或具有洛伦兹不变性破坏的最小耦合标量场具有这种能力。在后一种情况下，加速膨胀和幻影分界线交叉是这种洛伦兹破坏场景的相互作用性质的结果。
Possible test of local Lorentz invariance from $τ$ decays
我们分析了从τ衰变的观测中检验局部洛伦兹不变性的可能性。未来的前景进行了讨论的探测距离低于电弱特征标度。
Cosmic messengers (gamma rays, cosmic rays, neutrinos and gravitational waves) provide a powerful complementary way to search for Lorentz invariance violating effects to laboratory-based experiments. The long baselines and high energies involved make Cherenkov telescopes, air-shower arrays, neutrino telescopes and gravitational wave detectors unique tools to probe the expected tiny effects that the breaking of Lorentz invariance would cause in the propagation of these messengers, in comparison with the standard scenario. In this chapter we explain the expected effects that the mentioned detect…
Cosmology in the Lorentz gauge theory
本文介绍洛伦兹规范理论在宇宙学中的应用，通过自发对称破缺（khronogenesis）描述时空涌现，预言暴胀，并允许一致描述自旋流，为ΛCDM宇宙学提供要素。
Crossing of the Phantom Divided Barrier with Lorentz Invariance Violating Fields
本文研究了洛伦兹不变性破坏的暗能量模型中可能的幻影分割势垒穿越。洛仑兹不变性破坏是通过在作用量中引入一个矢量场来实现的，它直接包含在标量场和状态方程的动力学中。这个有趣的功能，使我们能够研究幻影分割障碍跨越的背景下，洛伦兹不变性违反。结果表明，在适当的参数空间选择下，物态方程可以仅通过一个标量场穿越幻分势垒，而洛伦兹破坏矢量场控制着这一穿越。
A Lorentz Invariance Violating Cosmology on the DGP Brane
我们研究违反DGP启发的膜世界场景的洛伦兹不变性的宇宙学意义。一个最小的耦合标量场和一个单一的，固定的范数，违反洛伦兹类时矢量场内的互动图片提供了一个广泛的参数空间，占后期的时间加速和过渡到幻影相位的标量场。
Tests of Lorentz invariance: a 2013 update
我们提出了一个更新的审查洛伦兹不变性测试在有效场论（EFT）的问题，以及在重力部门。经过一般性的讨论的作用，洛伦兹不变性和推导其转换沿所谓的冯Ignatovski定理，我们提出的动力学框架内开发的本地EFT和可用的约束参数的洛伦兹断裂效应。最后，我们讨论了两个具体的例子，OPERA“事件”和Hoelava-Lifshitz引力的情况。第一种情况将作为一个例子，并警告，实际应用的一般技术开发的约束洛伦兹不变性破坏（LIV）的直接观察可能显示这些影响。第二个案例将展示同样的技术在特定的量子引力场景中的应用如何具有在纯现象学的EFT方法中不可预见的深远影响。
Truly Lorentzian quantum cosmology
本文提出将迷你超空间路径积分限制在正尺度因子平方的洛伦兹构型上，发现这能显著改变期望值、实现奇点避免，并表明半经典鞍点近似并非总是有效，需重新审视隧穿、无边界提议、反弹宇宙学及暴胀量子起源等相关工作。
On the local Lorentz invariance in N=1 supergravity
我们讨论了N=1超引力下的局部洛伦兹不变性，并表明以前试图用$γ-$矩阵来寻找洛伦兹约束的显式解是不正确的。我们改进了该解决方案，通过使用不同的表示的洛伦兹算子的旋转群的生成元，并显示其兼容性与矩阵表示的费米子场。我们发现最一般的波泛函，满足洛伦兹约束在这个表示。
Gauge invariance in Loop Quantum Cosmology : Hamilton-Jacobi and Mukhanov-Sasaki equations for scalar perturbations
研究了标量微扰的规范不变性和相应的运动方程。推广了在广义相对论框架下发展起来的方法，对圈量子宇宙学中的Hamilton-Jacobi方程进行了详细的研究。建立了规范不变观测量，并分别用哈密顿和拉格朗日方法讨论了它们的运动方程。这种方法适用于标量扰动与完整或逆体积校正。
Gauge-invariance in one-loop quantum cosmology
研究单圈量子宇宙学中的规范不变性和规范依赖性问题。我们提出了一些边界条件应满足的要求，以便给出规范无关的路径积分。QED的情况下进行了详细的研究。本文概述了有界区域内引力场规范不变量子化的困难。
Rotating Odd-Parity Lorentz Invariance Test in Electrodynamics
本文首次报道了在微波马赫-曾德尔干涉仪上进行电动力学中的旋转奇宇称洛伦兹不变性检验，该实验设置了$-0.3\pm 3\times10^{-7}$的$ κ_{tr}$的直接束缚。使用新的功率回收波导干涉仪技术（具有$2\times10^{-11} rad/\sqrt{Hz}$有史以来达到的最高光谱分辨率），我们表明在未来可以实现几个数量级的改进。
Testing Lorentz Invariance with a Double-Pass Optical Ring Cavity
我们已经开发了一个装置来测试洛伦兹不变性在光子扇区通过测量谐振频率之间的差异的两个反向传播的非对称光学环形腔使用双程配置。在$δc /c \lesssim 10^{-14}$一级没有发现违规的重大证据。我们的设备和最近的结果的细节。
New tests of local Lorentz invariance and local position invariance of gravity with pulsars
提出了新的测试，以约束可能的偏差从局部洛伦兹不变性和局部位置不变性的重力部门。通过使用两个二进制时钟的精确定时结果，PSR J1012+5307和J1738+0333，我们能够高精度地约束（强场）参数化后牛顿参数$\hatα_1$、$\hatα_2$、$\hatξ$，其中，$|\hatξ| < 3.1\times10^{-4}$（95%C.L.）在这里首次报道。
The Lorentz invariance and Einstein equivalence principle violating effects in the narrow 7.8 eV transition in 229Th nucleus may be 100 000 times larger than in atoms. This transition may be investigated using high precision laser spectroscopy methods, has a very small width, and suppressed systematic effects. Similar values of the effects are expected in 73 eV 235U nuclear transition which is coming within the reach of the laser spectroscopy. Mossbauer transitions give another possibility.
We consider three possible manifestations of physics beyond the Standard Model, and the relations among them. These are Lorentz non-invariance (LNI), violations of the Weak Equivalence Principle (WEP), and indications of time-varying nuclear decay constants. We present preliminary results from a new experiment indicating the presence of annual and subannual periodicities in decay data, and discuss their implications for physics beyond the Standard Model.
A search for sidereal variations in the non-Newtonian force between two tungsten plates separated at millimeter ranges sets experimental limits on Lorentz invariance violation involving quadratic couplings of Riemann curvature. We show that the Lorentz invariance violation force between two finite flat plates is dominated by the edge effects, which includes a suppression effect leading to lower limits than previous rough estimates. From this search, we determine the current best constraints of the Lorentz invariance violating coefficients at a level of $10^{-8}$ m$^{2}$.
A Five Dimensional Space Without Local Lorentz Invariance
研究了在局部洛伦兹变换下不具有不变性的五维空间，并引入了使理论不变性的变换。我们表明，洛伦兹力是包括在随后的运动方程。四维爱因斯坦方程和麦克斯韦方程组从场方程中产生，而齐次麦克斯韦方程组自然地出现在工作中。介绍了相应的量子理论。恢复了自由粒子和氢原子的光谱。研究了Schwarzschild空间的量子结构。
The Poincaré invariance of GR is usually interpreted as Lorentz invariance plus diffeomorphism invariance. In this paper, by introducing the local inertial coordinates (LIC), it is shown that a theory with Lorentz and diffeomorphism invariance is not necessarily Poincaré invariant. Actually, the energy-momentum conservation is violated there. On the other hand, with the help of the LIC, the Poincaré invariance is reinterpreted as an internal symmetry. In this formalism, the conservation law is derived, which has not been sufficiently explored before.
Lorentz Invariance and the Cosmological Constant
弦场论中的非平凡解可能导致洛伦兹不变性的自发破缺和新的张量-物质相互作用。有人认为，需要贡献的真空期望值的洛伦兹张量占真空能量的水平，$Ω_{0}^Λ = 0.5$意味着新的相互作用范围是$λ\sim 10^{-4} m$。这些对洛伦兹对称性的破坏与最严格的实验极限是一致的。
Recently, first limits on putative Lorentz invariance violation coefficients in the pure gravity sector were determined by the reanalysis of short-range gravity experiments. Such experiments search for new physics at sidereal frequencies. They are not, however, designed to optimize the signal strength of a Lorentz invariance violation force; in fact the Lorentz violating signal is suppressed in the planar test mass geometry employed in those experiments. We describe a short-range torsion pendulum experiment with enhanced sensitivity to possible Lorentz violating signals. A periodic, striped te…
Testing Lorentz Invariance Using an Odd-Parity Asymmetric Optical Resonator
我们提出了第一个实验测试的洛伦兹不变性使用之间的频率差的非对称奇宇称光学谐振腔中的反向传播模式。这种类型的测试是$\sim10^{4}$更敏感的奇宇称和各向同性（标量）违反洛伦兹不变性比等效的传统偶宇称实验，由于光学谐振腔的不对称性。奇宇称谐振器的缺点已经通过使用反向传播模式来消除，从而对环境波动提供高水平的免疫力。与非旋转实验，我们的结果限制各向同性洛伦兹违反参数$\tildeκ_{tr}$为3.4 $\pm$ 6.2 x $10^{-9}$，最好的报告约束从直接测量。使用这种技术的奇宇称和标量违反洛伦兹不变性的界限可以提高许多数量级。
Constraints on Lorentz Invariance Violation using INTEGRAL/IBIS observations of GRB041219A
洛伦兹不变性破坏的实验检验之一是测量起源于遥远宇宙学物体的光子的传播速度与螺旋度的关系。使用最近确定的距离的伽马射线暴GRB 041219 A，其中一个高度的偏振观察到的即时发射，我们能够提高4个数量级的现有约束洛伦兹不变性违反，所产生的真空双折射现象。
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