Deformed Spacetime

Geometrizing Interactions in Four and Five Dimensions

  • Fabio Cardone
  • Roberto Mignani

Part of the Fundamental Theories of Physics book series (FTPH, volume 157)

Table of contents

About this book


This volume provides a detailed discussion of the mathematical aspects and the physical applications of a new geometrical structure of space-time, based on a generalization ("deformation") of the usual Minkowski space, as supposed to be endowed with a metric whose coefficients depend on the energy.
Such a formalism (Deformed Special Relativity, DSR) allows one

  • to account for breakdown of local Lorentz invariance in the usual, special-relativistic meaning (however, Lorentz invariance is recovered in a generalized sense)
  • to provide an effective geometrical description of the four fundamental interactions (electromagnetic, weak, strong and gravitational)

Moreover, the four-dimensional energy-dependent space-time is just a manifestation of a larger, five-dimensional space in which energy plays the role of a fifth (non-compactified) dimension. This new five-dimensional scheme (Deformed Relativity in Five Dimensions, DR5) represents a true generalization of the usual Kaluza-Klein (KK) formalism.
The mathematical properties of such a generalized KK scheme are illustrated. They include the solutions of the five-dimensional Einstein equations in vacuum in most cases of physical relevance, the infinitesimal symmetries of the theory for the phenomenological metrics of the four interactions, and the study of the five-dimensional geodesics.
The mathematical results concerning the geometry of the deformed five-dimensional spacetime (like its Killing symmetries) can be applied also to other multidimensional theories with infinite extra dimensions.
Some experiments providing preliminary evidence for the hypothesized deformation of space-time for all the four fundamental interactions are discussed.

Graduate students and researchers in mathematics and physics; researchers and engineers working in nuclear and space industries, space agencies, governmental scientific (including military and defense) institutions.


CERN Gravity LED Lidar Minkowski space RMS Relativity SR Special relativity electromagnetic wave

Authors and affiliations

  • Fabio Cardone
    • 1
  • Roberto Mignani
    • 2
  1. 1.Consiglio Nazionale delle RicercheItaly
  2. 2.Università Roma TreItaly

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 2007
  • Publisher Name Springer, Dordrecht
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-1-4020-6282-7
  • Online ISBN 978-1-4020-6283-4
  • Buy this book on publisher's site