Overview
- 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- Provides a detailed discussion of the mathematical aspects of the formalism, including some new, unpublished results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 book series: Fundamental Theories of Physics (FTPH, volume 157)
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Table of contents (26 chapters)
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Front Matter
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Physics Of Deformed Space-Time
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Front Matter
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Mathematics Of Deformed Space–Time
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Front Matter
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Experiments On Deformed Space–Time
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Front Matter
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Keywords
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)
Authors and Affiliations
Bibliographic Information
Book Title: Deformed Spacetime
Book Subtitle: Geometrizing Interactions in Four and Five Dimensions
Authors: Fabio Cardone, Roberto Mignani
Series Title: Fundamental Theories of Physics
DOI: https://doi.org/10.1007/978-1-4020-6283-4
Publisher: Springer Dordrecht
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Science+Business Media B.V. 2007
Hardcover ISBN: 978-1-4020-6282-7Published: 08 August 2007
Softcover ISBN: 978-90-481-7595-6Published: 30 November 2010
eBook ISBN: 978-1-4020-6283-4Published: 04 September 2007
Series ISSN: 0168-1222
Series E-ISSN: 2365-6425
Edition Number: 1
Number of Pages: XVIII, 506
Topics: Particle and Nuclear Physics, Classical Electrodynamics, Applications of Mathematics, Mathematical Methods in Physics, Classical and Quantum Gravitation, Relativity Theory, Quantum Field Theories, String Theory