Table of Contents
Physics Research International
Volume 2011, Article ID 302164, 9 pages
Research Article

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

1Observatório do Valongo, Universidade Federal do Rio de Janeiro, 20080-090 Rio de Janeiro, RJ, Brazil
2Departamento de Matemática, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC, Brazil

Received 30 September 2010; Accepted 3 January 2011

Academic Editor: Myung Kim

Copyright © 2011 Alexandre Lyra and Marcelo Carvalho. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.