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- Title
Special Relativity and Its Newtonian Limit from a Group Theoretical Perspective.
- Authors
Kong, Otto C. W.; Payne, Jason
- Abstract
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.
- Subjects
EINSTEIN, Albert, 1879-1955; SPECIAL relativity (Physics); REPRESENTATIONS of groups (Algebra); APPROXIMATION theory; PARTICLE dynamics; PHASE space; PARTICLE spin
- Publication
Symmetry (20738994), 2021, Vol 13, Issue 10, p1925
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym13101925