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Title: Relativity symmetries and Lie algebra contractions

Abstract

We revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions under a new perspective on what constitutes a relativity symmetry. Contractions of an SO(m,n) symmetry as an isometry on an m+n dimensional geometric arena which generalizes the notion of spacetime are discussed systematically. One of the key results is five different contractions of a Galilean-type symmetry G(m,n) preserving a symmetry of the same type at dimension m+n−1, e.g. a G(m,n−1), together with the coset space representations that correspond to the usual physical picture. Most of the results are explicitly illustrated through the example of symmetries obtained from the contraction of SO(2,4), which is the particular case for our interest on the physics side as the proposed relativity symmetry for “quantum spacetime”. The contractions from G(1,3) may be relevant to real physics.

Authors:
Publication Date:
OSTI Identifier:
22403470
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 351; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; LIE GROUPS; QUANTUM MECHANICS; RELATIVITY THEORY; SPACE-TIME

Citation Formats

Cho, Dai-Ning, and Kong, Otto C.W., E-mail: otto@phy.ncu.edu.tw. Relativity symmetries and Lie algebra contractions. United States: N. p., 2014. Web. doi:10.1016/J.AOP.2014.09.005.
Cho, Dai-Ning, & Kong, Otto C.W., E-mail: otto@phy.ncu.edu.tw. Relativity symmetries and Lie algebra contractions. United States. https://doi.org/10.1016/J.AOP.2014.09.005
Cho, Dai-Ning, and Kong, Otto C.W., E-mail: otto@phy.ncu.edu.tw. 2014. "Relativity symmetries and Lie algebra contractions". United States. https://doi.org/10.1016/J.AOP.2014.09.005.
@article{osti_22403470,
title = {Relativity symmetries and Lie algebra contractions},
author = {Cho, Dai-Ning and Kong, Otto C.W., E-mail: otto@phy.ncu.edu.tw},
abstractNote = {We revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions under a new perspective on what constitutes a relativity symmetry. Contractions of an SO(m,n) symmetry as an isometry on an m+n dimensional geometric arena which generalizes the notion of spacetime are discussed systematically. One of the key results is five different contractions of a Galilean-type symmetry G(m,n) preserving a symmetry of the same type at dimension m+n−1, e.g. a G(m,n−1), together with the coset space representations that correspond to the usual physical picture. Most of the results are explicitly illustrated through the example of symmetries obtained from the contraction of SO(2,4), which is the particular case for our interest on the physics side as the proposed relativity symmetry for “quantum spacetime”. The contractions from G(1,3) may be relevant to real physics.},
doi = {10.1016/J.AOP.2014.09.005},
url = {https://www.osti.gov/biblio/22403470}, journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = ,
volume = 351,
place = {United States},
year = {Mon Dec 15 00:00:00 EST 2014},
month = {Mon Dec 15 00:00:00 EST 2014}
}