3 + 1)维系统中超光速粒子的广义变换关系

IF 1.6 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Vivek Kumar Srivastava, Alok Kumar Verma, Garima Vaish
{"title":"3 + 1)维系统中超光速粒子的广义变换关系","authors":"Vivek Kumar Srivastava, Alok Kumar Verma, Garima Vaish","doi":"10.1007/s12648-024-03379-x","DOIUrl":null,"url":null,"abstract":"<p>Here, we have proposed new transformation relations between two inertial frames with relative velocity greater than speed of light and discussed the required conditions to detect superluminal particles in the physical realm. A novel theoretical formulation is conceptualized to uniquely depict the frame of reference, valid for all ranges of velocities, in a complex plane. In the tachyonic regime, the super-relativistic gamma factor is obtained by parameterizing the generalised gamma factor using the complementary frames of reference of superluminal and subluminal spaces. The formulations of transformation relations have been analysed in four different classes, i.e., two inter and two intra classes of frames, for subluminal and superluminal particles. The intra classes of frames encompass real gamma factors, whilst, inter classes of frames involve imaginary gamma factors. These transformation relations in all four different classes are expressed in 4-vector form with their respective transformation matrices <span>\\((\\Lambda )\\)</span> and are found to be invariant under the transformations. This invariancy has led to the establishment of relationships among the transformation factors in stationary and moving frames. The velocity 4-vector relations for subluminal and superluminal particles, both in moving and stationary frames, have been evaluated. The 4-velocity transformation relations between particle velocity in stationary and moving frames are also introduced by using the transformation matrices. Based on these 4-velocity transformations, relative velocity addition relations have been deduced and discussed corresponding to each of the transformation relations. The generalised gamma factor has been concluded and validated for both frames of reference.</p>","PeriodicalId":584,"journal":{"name":"Indian Journal of Physics","volume":"53 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalised transformation relations for superluminal particles in (3 + 1) dimensional system\",\"authors\":\"Vivek Kumar Srivastava, Alok Kumar Verma, Garima Vaish\",\"doi\":\"10.1007/s12648-024-03379-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Here, we have proposed new transformation relations between two inertial frames with relative velocity greater than speed of light and discussed the required conditions to detect superluminal particles in the physical realm. A novel theoretical formulation is conceptualized to uniquely depict the frame of reference, valid for all ranges of velocities, in a complex plane. In the tachyonic regime, the super-relativistic gamma factor is obtained by parameterizing the generalised gamma factor using the complementary frames of reference of superluminal and subluminal spaces. The formulations of transformation relations have been analysed in four different classes, i.e., two inter and two intra classes of frames, for subluminal and superluminal particles. The intra classes of frames encompass real gamma factors, whilst, inter classes of frames involve imaginary gamma factors. These transformation relations in all four different classes are expressed in 4-vector form with their respective transformation matrices <span>\\\\((\\\\Lambda )\\\\)</span> and are found to be invariant under the transformations. This invariancy has led to the establishment of relationships among the transformation factors in stationary and moving frames. The velocity 4-vector relations for subluminal and superluminal particles, both in moving and stationary frames, have been evaluated. The 4-velocity transformation relations between particle velocity in stationary and moving frames are also introduced by using the transformation matrices. Based on these 4-velocity transformations, relative velocity addition relations have been deduced and discussed corresponding to each of the transformation relations. The generalised gamma factor has been concluded and validated for both frames of reference.</p>\",\"PeriodicalId\":584,\"journal\":{\"name\":\"Indian Journal of Physics\",\"volume\":\"53 1\",\"pages\":\"\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-08-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indian Journal of Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s12648-024-03379-x\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indian Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s12648-024-03379-x","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0

摘要

在此,我们提出了两个相对速度大于光速的惯性框架之间的新变换关系,并讨论了在物理领域探测超光速粒子所需的条件。我们概念化了一种新的理论表述,在复平面上唯一地描述了对所有速度范围都有效的参照系。在超光速体系中,超相对论伽马因子是通过使用超光速和亚光速空间的互补参照系对广义伽马因子进行参数化而获得的。针对亚流星粒子和超流星粒子,我们分析了四类不同的变换关系,即两类帧间变换关系和两类帧内变换关系。帧内类包括实伽马因子,而帧间类涉及虚伽马因子。所有四个不同类别中的这些变换关系都用各自的变换矩阵 \((\Lambda )\) 以 4 向量形式表示,并发现它们在变换下是不变的。这种不变性导致了静止和运动帧中变换因子之间关系的建立。对亚流星粒子和超流星粒子在运动帧和静止帧中的速度四矢量关系进行了评估。此外,还利用变换矩阵引入了静止帧和运动帧中粒子速度之间的 4 速度变换关系。根据这些四速度变换,推导并讨论了与每个变换关系相对应的相对速度加法关系。得出了广义伽马因子,并对两种参照系进行了验证。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Generalised transformation relations for superluminal particles in (3 + 1) dimensional system

Generalised transformation relations for superluminal particles in (3 + 1) dimensional system

Here, we have proposed new transformation relations between two inertial frames with relative velocity greater than speed of light and discussed the required conditions to detect superluminal particles in the physical realm. A novel theoretical formulation is conceptualized to uniquely depict the frame of reference, valid for all ranges of velocities, in a complex plane. In the tachyonic regime, the super-relativistic gamma factor is obtained by parameterizing the generalised gamma factor using the complementary frames of reference of superluminal and subluminal spaces. The formulations of transformation relations have been analysed in four different classes, i.e., two inter and two intra classes of frames, for subluminal and superluminal particles. The intra classes of frames encompass real gamma factors, whilst, inter classes of frames involve imaginary gamma factors. These transformation relations in all four different classes are expressed in 4-vector form with their respective transformation matrices \((\Lambda )\) and are found to be invariant under the transformations. This invariancy has led to the establishment of relationships among the transformation factors in stationary and moving frames. The velocity 4-vector relations for subluminal and superluminal particles, both in moving and stationary frames, have been evaluated. The 4-velocity transformation relations between particle velocity in stationary and moving frames are also introduced by using the transformation matrices. Based on these 4-velocity transformations, relative velocity addition relations have been deduced and discussed corresponding to each of the transformation relations. The generalised gamma factor has been concluded and validated for both frames of reference.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Indian Journal of Physics
Indian Journal of Physics 物理-物理:综合
CiteScore
3.40
自引率
10.00%
发文量
275
审稿时长
3-8 weeks
期刊介绍: Indian Journal of Physics is a monthly research journal in English published by the Indian Association for the Cultivation of Sciences in collaboration with the Indian Physical Society. The journal publishes refereed papers covering current research in Physics in the following category: Astrophysics, Atmospheric and Space physics; Atomic & Molecular Physics; Biophysics; Condensed Matter & Materials Physics; General & Interdisciplinary Physics; Nonlinear dynamics & Complex Systems; Nuclear Physics; Optics and Spectroscopy; Particle Physics; Plasma Physics; Relativity & Cosmology; Statistical Physics.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信