Non-Linear Relativity in Position Space

Details Non-Linear Relativity in Position Space Non-Linear Relativity in Position Space

2003-03-18

arxiv.org/abs/gr-qc/0303067v2

Phys.Rev. D70 (2004) 084007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, revised version

Scientific paper

10.1103/PhysRevD.70.084007

We propose two methods for obtaining the dual of non-linear relativity as previously formulated in momentum space. In the first we allow for the (dual) position space to acquire a non-linear representation of the Lorentz group independently of the chosen representation in momentum space. This requires a non-linear definition for the invariant contraction between momentum and position spaces. The second approach, instead, respects the linearity of the invariant contraction. This fully fixes the dual of momentum space and dictates a set of energy-dependent space-time Lorentz transformations. We discuss a variety of physical implications that would distinguish these two strategies. We also show how they point to two rather distinct formulations of theories of gravity with an invariant energy and/or length scale.

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