Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2012-01-16
Physics
High Energy Physics
High Energy Physics - Theory
42 pages and 4 figures
Scientific paper
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 of causal events in flat nD spacetime. Its general structure and field-theoretic representations are described, 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 the roles played by the ghost dilation field and physical scalar fields is evidenced. Hyperbolic coordinates of various types are introduced for the purpose of providing different but equivalent representations of physical systems, respectively grounded on the Riemann or Cartan manifold, mainly in view of further studies. Lastly, the Lagrangian theory of Higgs fields interacting with dilation field in a conformally flat 4D spacetime, as well as their motion equations and energy-momentum tensors, are described for both Riemann- and Cartan-manifold representations, in view of the detailed study of Higgs-field dynamics, which will be illustrated in the third paper.
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