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I need help in understanding the elements of a paper that I think could turn out to be quite important, namely http://arxiv.org/abs/0711.2274 de Sitter Relativity: a New Road to Quantum Gravity

R. Aldrovandi, J. G. Pereira)

Inter aliathey say that:

in de Sitter relativity “...... conformal transformations will naturally be incorporated in the kinematics of spacetime, and the corresponding conformal current will appear as part of the Noether conserved current [7].” This is because “ .... a cosmological term naturally introduces the conformal generators in the definition of spacetime transitivity.”

I understand (probably wrongly) that the main feature of conformal transformations is that they are shape-preserving on a small enough scale. If this is so, I have a question:

Lorentz transformations are not shape-preserving; the Lorentz contaction is uniaxial, as in the explanation of the null-result of the Michelson-Morley experiment.

Are the conformal transformations of de Sitter SR bolt-on additions that leave Lorentz contraction intact, while providing dilation via a non-zero cosmological constant?

And also, what exactly is the "proper conformal current" they talk of? Is it a sort of extra momentum-energy flux?

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# De Sitter relativity and Lorentz contraction

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