Special relativity and its newtonian limit from a group theoretical perspective

Otto C.W. Kong, Jason Payne

研究成果: 雜誌貢獻回顧評介論文同行評審

1 引文 斯高帕斯(Scopus)

摘要

In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting point of the formulation is the representations of the relativity symmetries. Moreover, that seriously furnishes—via the notion of symmetry contractions— a natural way in which one can understand how the Newtonian theory arises as an approximation to Einstein’s theory. We begin with the Poincaré symmetry underlying special relativity and the nature of Minkowski spacetime as a coset representation space of the algebra and the group. Then, we proceed to the parallel for the phase space of a spin zero particle, in relation to which we present the full scheme for its dynamics under the Hamiltonian formulation, illustrating that as essentially the symmetry feature of the phase space geometry. Lastly, the reduction of all that to the Newtonian theory as an approximation with its space-time, phase space, and dynamics under the appropriate relativity symmetry contraction is presented. While all notions involved are well established, the systematic presentation of that story as one coherent picture fills a gap in the literature on the subject matter.

原文???core.languages.en_GB???
文章編號1925
期刊Symmetry
13
發行號10
DOIs
出版狀態已出版 - 10月 2021

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