Conformal and projective symmetries in Newtonian cosmology

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• 作者：C. Duval^a ; ^{duval@cpt.univ-mrs.fr} ; G.W. Gibbons^b ; ^{G.W.Gibbons@damtp.cam.ac.uk} ; P.A. Horvá ; thy^c ; ^d ; ^{horvathy@lmpt.univ-tours.fr}
• 关键词：Conformal Newton&ndash ; Carton group ; Conformal Bargmann group ; Newtonian cosmology ; Newton&ndash ; Hooke solution
• 刊名：Journal of Geometry and Physics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：112
• 期：Complete
• 页码：197-209
• 全文大小：520 K
• 卷排序：112

文摘

Definitions of non-relativistic conformal transformations are considered both in the Newton–Cartan and in the Kaluza–Klein-type Eisenhart/Bargmann geometrical frameworks. The symmetry groups that come into play are exemplified by the cosmological, and also the Newton–Hooke solutions of Newton’s gravitational field equations. It is shown, in particular, that the maximal symmetry group of the standard cosmological model is isomorphic to the 1313-dimensional conformal-Newton–Cartan group whose conformal-Bargmann extension is explicitly worked out. Attention is drawn to the appearance of independent space and time dilations, in contrast with the Schrödinger group or the Conformal Galilei Algebra.