Deformed Spacetime: Geometrizing Interactions in Four and Five Dimensions by Fabio CardoneDeformed Spacetime: Geometrizing Interactions in Four and Five Dimensions by Fabio Cardone

Deformed Spacetime: Geometrizing Interactions in Four and Five Dimensions

byFabio Cardone, Roberto Mignani

Paperback | November 30, 2010

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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 oneto 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.
Title:Deformed Spacetime: Geometrizing Interactions in Four and Five DimensionsFormat:PaperbackDimensions:524 pagesPublished:November 30, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:904817595X

ISBN - 13:9789048175956

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Table of Contents

Part I: Physics of Deformed Space-TimePart II: Mathematics of Deformed Space-TimePart III: Experimental Arguments for Deformed Space-TimePart IV: Deformed Space-Time in Five Dimensions: GeometryPart V: Deformed Space-Time in Five Dimensions: DynamicsAppendix A: Reductivity of the Ү-Hypothesisfor the 12 Classes of the vacuum Einstein Equations in the Power Ansatz.Appendix B: Gravitational Killing Symmetries for Special Forms of b12(x5)and b22(x5)Appendix C: Explicit and Implicit Forms of geodesics for the 12 Classesof Solutions of Einstein's Equations in Vacuum in the Power Ansatz.

Editorial 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)