none Lie Algebra Contraction and Relativity Symmetries

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:	[Graduate Institute of Physics] Electronic Thesis & Dissertation

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