Conformal transformations and Clifford algebras

Author:

Lounesto Pertti,Latvamaa Esko

Abstract

A spinor representation for the conformal group of the real orthogonal space R p , q {R^{p,q}} is given. First, the real orthogonal space R p , q {R^{p,q}} is compactified by adjoining a (closed) isotropic cone at infinity. Then the nonlinear conformal transformations are linearized by regarding the conformal group as a factor group of a larger orthogonal group. Finally, the spin covering group of this larger orthogonal group is realized in the Clifford algebra R 1 + p , q {R_{1 + p,q}} containing the Clifford algebra R p , q {R_{p,q}} on the orthogonal space R p , q {R^{p,q}} . Explicit formulas for orthogonal transformations, translations, dilatations and special conformal transformations are given in Clifford language.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference8 articles.

1. Clifford modules;Atiyah, M. F.;Topology,1964

2. The Algebraic Theory of Spinors

3. J. Haantjes, Conformal representations of an n-dimensional euclidean space with a non-definite fundamental form on itself, Nederl. Akad. Wetensch. Proc. 40 (1937), 700-705.

4. Grundlehren der Mathematischen Wissenschaften, Band 226;Karoubi, Max,1978

5. Zur Physikalischen Deutung und darstellungsthoretischen Analyse der konformen Transformationen von Raum und Zeit;Kastrup, H. A.;Ann. Physik (7),1961

Cited by 19 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Clifford Analysis for Higher Spin Operators;Operator Theory;2015

2. Kravchuk Polynomials and Induced/Reduced Operators on Clifford Algebras;Complex Analysis and Operator Theory;2014-05-06

3. Clifford Analysis for Higher Spin Operators;Operator Theory;2014

4. Delambre–Gauss formulas for augmented, right-angled hexagons in hyperbolic 4-space;Advances in Mathematics;2012-06

5. Quaternlonic möbius transformations and loxodromes;Complex Variables, Theory and Application: An International Journal;1998-11

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3