{"title":"Deformed Lorentz Symmetry and Corresponding Geometry in Ultra-High Energy Astrophysics","authors":"G. Ter-Kazarian","doi":"10.1134/S0202289324010122","DOIUrl":null,"url":null,"abstract":"<p>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, <i>master space</i> (MS<span>\\({}_{p}\\)</span>) induced supersymmetry, subject to certain rules. We derive the Standard Lorentz Code (SLC) in a new perspective of global double MS<span>\\({}_{p}\\)</span>-SUSY transformations in terms of Lorentz spinors (<span>\\(\\underline{\\theta},\\underline{\\bar{\\theta}}\\)</span>) referred to MS<span>\\({}_{p}\\)</span>. The MS<span>\\({}_{p}\\)</span>, embedded in the background 4D-space, is an <i>unmanifested</i> indispensable individual companion to the particle of interest as the intrinsic property devoid of any external influence. While all particles are living on <span>\\(M_{4}\\)</span>, their superpartners can be viewed as living on MS<span>\\({}_{p}\\)</span>. In the sequel, we turn to the deformation of these spinors: <span>\\(\\underline{\\theta}\\to\\underline{\\tilde{\\theta}}=\\lambda^{1/2}\\,\\underline{\\theta}\\)</span>, etc., where <span>\\(\\lambda\\)</span> appears as a deformation scalar function of the Lorentz invariance (LIDF). This yields both the DLE and DMAV, respectively, in the form <span>\\(\\tilde{ds}=\\lambda ds\\)</span> and <span>\\(\\tilde{c}=\\lambda c\\)</span>, 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<span>\\({}_{p}\\)</span>-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-<span>\\(\\gamma\\)</span> 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.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Gravitation and Cosmology","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S0202289324010122","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
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.
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