Generalized Minkowski Spaces and Killing Symmetries

In the first Part of this book, we discussed the physical foundations of the DSR in four dimensions. This second Part will be devoted to dealing in detail with the mathematical features and properties of DSR. In this framework, the isometries of the deformed Minkowski space ^ãM play a basic role. The mathematical tool needed to such a study are the Killing equations, whose solution will allow us to determine both the infinitesimal and the finite structure of the deformed chronotopical groups of symmetries [41–43]. An important result we shall report at the end of this Part – due to its physical implications – is the geometrical structure of ^ãM as a generalized Lagrange space [12, 13, 44].