The Conformal Universe II: Conformal Symmetry, its Spontaneous Breakdown and Higgs Fields in Conformally Flat Spacetime

摘要

This is the second of a series of three papers on Conformal General Relativity.The conformal group is here introduced as the invariance group of the partial ordering ofcausal events in flat nD spacetime. Its general structure and field–theoretic representations aredescribed, with particular emphasis on the remarkable properties of orthochronous inversions.Discrete symmetries and field representations in flat 4D spacetime are described in details.The spontaneous breakdown of global and local conformal symmetry is then discussed and theroles played by the ghost dilation field and physical scalar fields are evidenced. Hyperboliccoordinates of various types are introduced for the purpose of providing different but equivalentrepresentations of physical systems, respectively grounded on the Riemann manifold and theCartan manifold, mainly in view of further studies. Lastly, the Lagrangian theory of Higgsfields interacting with dilation field in a conformally flat 4D spacetime, as well as their motionequations and energy–momentum tensors, are described for both Riemann– and Cartan–manifold representations, in view of the detailed study of Higgs–field dynamics, which willbe illustrated in the third paper.