Possible role of symmetry in physics and cosmology (a contribution to platonism)

摘要

After a short review of the main concepts of the theory of continuous groups of transformations, the role of Lorentz and Poincare groups in the discovery of the relativistic revolution and of Minkowski space-time is presented. The properties of the conformal group and its possible connection with the cosmological principle are discussed. A short description of recently discovered large scale structures of distant galaxies in the universe and their interpretation as spontaneous violation of the conformal group of symmetry, or of the cosmological principle, and their analogy with the geometry of the H-atom in momentum space, is given. The possibility that, if both space-time and momentum space are conformally compactified, the difficult concepts of infinity and infinitesimal might be eliminated from the tools for understanding nature, is investigated. 14 refs, 2 figs. (Atomindex citation 26:068041)