Deformed Lorentz Symmetry and Corresponding Geometry in Ultra-High Energy Astrophysics

IF 1.2 4区 物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS Gravitation and Cosmology Pub Date : 2024-04-04 DOI:10.1134/S0202289324010122
G. Ter-Kazarian
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Abstract

This paper purports to develop a consistent microscopic theory of deformed Lorentz symmetry and the corresponding deformed geometry. Among the key geometric predictions of this approach, one lies in both the deformed line element (DLE) and the deformed maximum attainable velocity (DMAV) of a particle leading to potentially observable signatures in ultra-high energy astrophysics. In particular, the DMAV has in the past often been tested in a phenomenological approach to cosmic-ray and astrophysical-photon physics in order to extract constraints on those velocities. To this aim, we develop the theory of, so-called, master space (MS\({}_{p}\)) induced supersymmetry, subject to certain rules. We derive the Standard Lorentz Code (SLC) in a new perspective of global double MS\({}_{p}\)-SUSY transformations in terms of Lorentz spinors (\(\underline{\theta},\underline{\bar{\theta}}\)) referred to MS\({}_{p}\). The MS\({}_{p}\), embedded in the background 4D-space, is an unmanifested indispensable individual companion to the particle of interest as the intrinsic property devoid of any external influence. While all particles are living on \(M_{4}\), their superpartners can be viewed as living on MS\({}_{p}\). In the sequel, we turn to the deformation of these spinors: \(\underline{\theta}\to\underline{\tilde{\theta}}=\lambda^{1/2}\,\underline{\theta}\), etc., where \(\lambda\) appears as a deformation scalar function of the Lorentz invariance (LIDF). This yields both the DLE and DMAV, respectively, in the form \(\tilde{ds}=\lambda ds\) and \(\tilde{c}=\lambda c\), provided the invariance of DLE, and the same value of DMAV in free space holds for all inertial systems. Thus the LID (Lorentz invariance deformation) generalization of global MS\({}_{p}\)-SUSY theory formulates the generalized relativity postulates in a way that preserve the relativity of inertial frames, in spite of the appearance of modified terms in the LID dispersion relations. We complement this conceptual investigation with testing of various LIDFs in the UHECR- and TeV-\(\gamma\) threshold anomalies by implications for several scenarios: the Coleman and Glashow-type perturbative extension of SLC, the LID extension of standard model, the LID in quantum gravity motivated space-time models, the LID in loop quantum gravity models, and the LID for the models preserving the relativity of inertial frames.

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超高能天体物理学中的变形洛伦兹对称性和相应几何图形
摘要 本文旨在发展变形洛伦兹对称性和相应变形几何的一致微观理论。这种方法的关键几何预言之一是粒子的变形线元(DLE)和变形最大可达到速度(DMAV),这将导致超高能天体物理学中潜在的可观测特征。特别是,在宇宙射线和天体物理光子物理学的现象学方法中,过去经常对 DMAV 进行测试,以提取对这些速度的约束。为此,我们发展了所谓的主空间(MS\({}_{p}\))诱导超对称理论,并遵循一定的规则。我们从全局双 MS\({}_{p}\)-SUSY 变换的新角度推导出了标准洛伦兹编码(SLC),它是以洛伦兹旋量(\(\underline/{theta},\underline/{bar/{theta}}\))为参照的MS\({}_{p}\)。MS({}_{p}\)嵌入到背景4D空间中,是感兴趣的粒子的一个未显现的不可或缺的个体伴生体,它是粒子的固有属性,不受任何外部影响。当所有粒子都生活在 \(M_{4}\) 上时,它们的超级伙伴可以被视为生活在 MS\({}_{p}\) 上。接下来,我们将讨论这些旋量的变形:\(\underline{theta}\to\underline{tilde{theta}}=\lambda^{1/2}\,\underline{theta}\)等等,其中\(\lambda\)作为洛伦兹不变性(LIDF)的变形标量函数出现。这就产生了DLE和DMAV,其形式分别为\(\tilde{ds}=\lambda ds\) 和\(\tilde{c}=\lambda c\) ,前提是DLE的不变性和自由空间中DMAV的相同值对所有惯性系都成立。因此,全局MS({}_{p}\)-SUSY理论的LID(洛伦兹不变性变形)广义制定了广义相对论公设,尽管在LID色散关系中出现了修正项,但它保留了惯性框架的相对性。我们通过对UHECR-和TeV-(\gamma\)阈值反常中的各种LIDFs的测试来补充这一概念性研究,这些测试涉及几种情况:SLC的Coleman和Glashow型微扰扩展、标准模型的LID扩展、量子引力动机时空模型中的LID、环量子引力模型中的LID以及保留惯性框架相对性的模型的LID。
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来源期刊
Gravitation and Cosmology
Gravitation and Cosmology ASTRONOMY & ASTROPHYSICS-
CiteScore
1.70
自引率
22.20%
发文量
31
审稿时长
>12 weeks
期刊介绍: Gravitation and Cosmology is a peer-reviewed periodical, dealing with the full range of topics of gravitational physics and relativistic cosmology and published under the auspices of the Russian Gravitation Society and Peoples’ Friendship University of Russia. The journal publishes research papers, review articles and brief communications on the following fields: theoretical (classical and quantum) gravitation; relativistic astrophysics and cosmology, exact solutions and modern mathematical methods in gravitation and cosmology, including Lie groups, geometry and topology; unification theories including gravitation; fundamental physical constants and their possible variations; fundamental gravity experiments on Earth and in space; related topics. It also publishes selected old papers which have not lost their topicality but were previously published only in Russian and were not available to the worldwide research community
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