Six new mechanics corresponding to further shape theories (Q2809082)

In this physics paper the author constructs three new relational physical theories what he calls (i) \textit{conformal shape mechanics}, (ii) \textit{area ratio} alias \textit{affine shape mechanics} and (iii) \textit{affine scale-and-shape mechanics}. The author also analyses classical gravity (general relativity theory) and its supersymmetric generalizations (supergravity theories) from the relational viewpoint paying special attention to the manifestation of background independence in these theories.NEWLINENEWLINEIn contemporary theoretical physics there is a renaissance of the Leibniz-Machian idea which tries to offer a description of physical reality without referring to an independently or physically existing absolute or physical space-time. These concepts are rather replaced with the relative positions or relations among the participating physical entities. Consequently in these theories instead of space and/or time, various configuration spaces play a role (see e.g. [\textit{J. Barbour}, The end of time. The next revolution in our understanding of the universe. Oxford: Oxford University Press (2000; Zbl 0971.83001)]). These considerations are in opposition with the more conventional Newton-Einsteinian concept which regards space and time as absolute or physical entities.