© 2007

Deformed Spacetime

Geometrizing Interactions in Four and Five Dimensions


  • Provides a unique and exhaustive exposition of the theory of deformed spacetime, developed in the last 15 years, both in four and five dimensions

  • Provides a detailed discussion of the mathematical aspects of the formalism, including some new, unpublished results

  • Provides a thorough account of the main experimental evidences for a possible deformed geometry of spacetime, including experiments in optics, gravity, cavitated fluids

  • Acquaints the reader with mathematical topics not usually considered in standard textbooks, like that of Generalized Lagrange Space

  • Provides the tools to develop technical applications from theory and experiments through the industrial spin-off


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

  1. 1.Consiglio Nazionale delle RicercheItaly
  2. 2.Università Roma TreItaly

Bibliographic information


From the reviews:

"This book deals with geometrizations of physical fields. The main emphasis is on theories with 4 and those with 5 space-time dimensions. Several types of deformations are considered … . Almost 90 pages are given to the appendices which contain a lot of formulas in several subcases for the material used in the book. Reference list and subject index close this monograph valuable for specialists interested in this type of alternatives to General Relativity Theory." (Hans-Jürgen Schmidt, Zentralblatt MATH, Vol. 1123 (1), 2008)