principle. Theories of this kind are called Doubly or Deformed Special Relativity (DSR).

Early examples were formulated in momentum space by the application of nonlinear representations of the Lorentz group to the energy and momentum of physical objects, such that there is an invariant value of energy and/or momentum of the order of the Planck energy and the Planck momentum. Technically this may be achieved by splitting energy/momentum variables into “physical" ones, usually denoted by $E$ and $\vec p$, and “pseudo"-variables (sometimes called platonic variables) $\varepsilon$ and $\vec\pi$, with both kinds of variables related by an invertible nonlinear transformation. Pseudo-variables satisfy the usual linear relations of SR, in consequence, the physical ones are acted upon by the (boost sector of the) Poincaré group in a deformed, nonlinear way. Note that the denomination ‘deformed’, common in the present context, denotes merely the action of the Lorentz group and has nothing to do with deformations of the Poincaré Lie algebra.

Pseudo-variables, although being mere auxiliary quantities in the construction of modified Lorentz transformations, have the following formal significance. Providing the linear representation of the Poincaré group, they carry the usual vector space structure of SR momentum space, whereas the space of $E$ 