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Fundamental Theories of Physics

Deformed Spacetime

Geometrizing Interactions in Four and Five Dimensions

Authors: Cardone, Fabio, Mignani, Roberto

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  • Provides an exhaustive exposition of the theory of deformed spacetime, in four and five dimensions
  • Discusses in detail the mathematical aspects of the formalism, including some new, unpublished results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
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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.

Audience:
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.

Reviews

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)


Table of contents (26 chapters)

Table of contents (26 chapters)
  • The Principle of Solidarity: Geometrical Descriptions of Interactions

    Pages 3-8

  • Description of Interactions by Energy-Dependent Metrics

    Pages 9-18

  • Deformed Special Relativity

    Pages 19-51

  • Metric Description of Interactions

    Pages 53-65

  • Generalized Minkowski Spaces and Killing Symmetries

    Pages 69-78

Buy this book

eBook n/a
  • ISBN 978-1-4020-6283-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-1-4020-6282-7
  • Free shipping for individuals worldwide
Softcover n/a
  • ISBN 978-90-481-7595-6
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Deformed Spacetime
Book Subtitle
Geometrizing Interactions in Four and Five Dimensions
Authors
Series Title
Fundamental Theories of Physics
Series Volume
157
Copyright
2007
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-1-4020-6283-4
DOI
10.1007/978-1-4020-6283-4
Hardcover ISBN
978-1-4020-6282-7
Softcover ISBN
978-90-481-7595-6
Series ISSN
0168-1222
Edition Number
1
Number of Pages
XVIII, 506
Topics