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.
General
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