A Geometrical Setting for Constructing Nonlinear Lorentz Transformations of the Albano-Dresden Type

الملخص EN

We investigate a nonlinear realization of the Lorentz transformation defined in 4-dimensional spacetime, and the corresponding invariant interval.

This new interval is not a quadratic form in the standard Minkowski spacetime, then we search for a description where it becomes a quadratic form in an infinite dimensional vector space.

In this extended space, we show how to generate two classes of nonlinear transformations, which form a group and interpret the non-linear transformation as compatible relations between atlas of a Lyra manifold.