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Deformed Spacetime

Part of the Fundamental Theories of Physics Book Series (volume 157)

DOI: 10.1007/978-1-4020-6283-4

ISBN: 978-1-4020-6282-7

Publisher: Springer Netherlands - Springer Journals

Jan 1, 2007

1 - 10 of 26 Chapters

Available

The Principle of Solidarity: Geometrical Descriptions of Interactions

Pages: 3 –8

[In 1955 the Italian mathematician Bruno Finzi, in his contribution to the book “Fifty Years of Relativity” [1], stated his “Principle of Solidarity” (PS), that sounds “It’s (indeed) necessary to consider space–time TO BE SOLIDLY CONNECTED with the physical phenomena occurring in it, so that its...
Available

Description of Interactions by Energy-Dependent Metrics

Pages: 9 –18

[We will now show how the dynamic role of the energy, in describing the structure of space–time, can be exploited in order to geometrize all four fundamental interactions, so to comply with the Finzi principle. As already stressed earlier, this can be achieved by suitably deforming space–time,...
Available

Deformed Special Relativity

Pages: 19 –51

[In order to develop the relativity theory in a deformed Minkowski space– time, one has to suitably generalize and clarify the basic concepts which are at the very foundation of SR.]
Available

Metric Description of Interactions

Pages: 53 –65

[We want now to review the results obtained for the deformed metrics, describing the four fundamental interactions – electromagnetic, weak, strong and gravitational –, from the phenomenological analysis of the experimental data. A more detailed treatment can be found in [6].]
Available

Generalized Minkowski Spaces and Killing Symmetries

Pages: 69 –78

[In the first Part of this book, we discussed the physical foundations of the DSR in four dimensions. This second Part will be devoted to dealing in detail with the mathematical features and properties of DSR. In this framework, the isometries of the deformed Minkowski space ãM play a basic role....
Available

Infinitesimal Structure of Generalized Space–Time Rotation Groups

Pages: 79 –98

[We shall now take advantage of the results derived in Chap. 5 on the Killing vectors of generalized N-d Minkowski spaces in order to study in detail the infinitesimal structure of their space–time rotation groups [41]. Needless to say, special emphasis will be given to the 4D case, and in...
Available

Finite Structure of Deformed Chronotopical Groups

Pages: 99 –153

[In Chap. 6, we discussed the infinitesimal structure of the chronotopical group of generalized Minkowski spaces and, in particular, of the deformed Minkowski space ãM(x5) of DSR.We want now to discuss the corresponding finite structure, so deriving in a rigorous way the DLT [42].]
Available

Deformed Space–Time Translations in Four Dimensions

Pages: 155 –169

[We want now to discuss the translational component of the generalized Poincaré group [43]. Without loss of generality, we shall consider the 4D case.]
Available

Deformed Minkowski Space as Generalized Lagrange Space

Pages: 171 –181

[We want now to show that the deformed Minkowski space ãM of DSR does possess another well-defined geometrical structure, besides the deformed metrical one. Precisely, we will show (following [44]) that ãM is a generalized Lagrange space.]
Available

Lorentz and CPT Symmetries in DSR

Pages: 185 –187

[One of the fundamental teachings of Einstein’s relativity theories is that the geometry of the (4D) space–time is globally curved (Riemannian) and locally flat (Minkowskian). This implies the existence of a local frame in which Special Relativity (SR) strictly holds for nongravitational...

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