THE AFFINE STRUCTURE OF GRAVITATIONAL THEORIES: SYMPLECTIC GROUPS AND GEOMETRY

DIEGO JULIO CIRILO; SALVATORE CAPOZZIELLO; MARIAFELICIA DE LAURENTIS

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS

WORLD SCIENTIFIC PUBL CO PTE LTD

Lugar: London, UK; Año: 2014

0219-8878

We give a geometrical description of gravitational theories from the viewpoint of sym- metries and affine structure. We show how gravity, considered as a gauge theory, can be consistently achieved by the nonlinear realization of the conformal-affine group in an indirect manner: due the partial isomorphism between CA(3, 1) and the centrally ex- tended Sp (8), we perform a nonlinear realization of the centrally extended (CE)Sp (8) in its semi-simple version. In particular, starting from the bundle structure of gravity, we derive the conformal-affine Lie algebra and then, by the non-linear realization, we define the coset field transformations, the Cartan forms and the inverse Higgs constrants. Fi- nally we discuss the geometrical Lagrangians where all the information on matter fields and their interactions can be contained.