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    Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/48266


    Title: none Lie Algebra Contraction and Relativity Symmetries
    Authors: 卓岱寧;Dai-Ning Cho
    Contributors: 物理研究所
    Keywords: 李代數;Cayley-Klein algebra;relativity symmetry;contraction;Lie algebra
    Date: 2011-09-27
    Issue Date: 2012-01-05 14:43:00 (UTC+8)
    Abstract: 變形(deformation)作為李代數的數學工具,於近來被應用於推導量子相對論(Quantum Relativity)及其對應之架構;而壓縮(contraction)是做為另外一個李代數之下的數學工具,乃為變形的相反運算。在這篇論文中,我們著重於壓縮的基本概念以及數種主要運算過程,並加以適當的範例作為演示。我們首先將壓縮應用在目前科學界熟悉的五維時空,並得到許多作為可能容納動力學的時空。再來我們將壓縮應用於量子相對論的架構,並得到許多與前述時空相呼應的可能容納動力學的幾何結構。 Deformation as a mathematical tool is used in deducing the recently developed Quantum Relativity and its framework, whereas contraction is the operation opposite to against deformation. In this dissertation we focus on and illustrate the idea of contraction and discuss several general approaches to contraction in detail. We first use contraction as an illustration in deducing the algebras of the so-called possible kinematical groups under the framework of the SO(1,4) and SO(2,3) groups. Then we apply contraction under the framework of Quantum Relativity (SO(2,4)) and examine the algebras we obtained that may be of the kinematical groups in its framework.
    Appears in Collections:[物理研究所] 博碩士論文

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