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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 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.
List of contents
Physics Of Deformed Space-Time.- The Principle of Solidarity: Geometrical Descriptions of Interactions.- Description of Interactions by Energy-Dependent Metrics.- Deformed Special Relativity.- Metric Description of Interactions.- Mathematics Of Deformed Space-Time.- Generalized Minkowski Spaces and Killing Symmetries.- Infinitesimal Structure of Generalized Space-Time Rotation Groups.- Finite Structure of Deformed Chronotopical Groups.- Deformed Space-Time Translations in Four Dimensions.- Deformed Minkowski Space as Generalized Lagrange Space.- Experiments On Deformed Space-Time.- Lorentz and CPT Symmetries in DSR.- Lorentz Invariance Breakdown: A Brief Survey.- Superluminal Propagation of Electromagnetic Waves.- The Shadow of Light: Lorentzian Violation of Electrodynamics in Photon Systems.- The Coil Experiment.- The Speed of Gravity.- Piezonuclear Reactions in Cavitated Water.- Piezonuclear Reactions in Cavitated Solutions.- Deformed Space-Time In Five Dimensions: Geometry.- Multidimensional Space-Time.- Embedding Deformed Minkowski Space in a 5D Riemann Space.- Einstein's Field Equations in R5 and Their Solutions.- Killing Equations in the Space R5.- Killing Symmetries for the 5D Metrics of Fundamental Interactions.- Deformed Space-Time In Five Dimensions: Dynamics.- Dynamics in DR5.- Solution of the Geodesic Equations in the Power Ansatz.- Complete Solutions of Geodesic Equations.- Conclusions and Perspectives.
Summary
This volume provides a detailed discussion of the mathematical aspects and 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. This new five-dimensional scheme (Deformed Relativity in Five Dimensions, DR5) represents a true generalization of the usual Kaluza-Klein (KK) formalism.
Additional text
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)
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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)
