he p - th ] 1 8 A ug 2 00 7 DSR and Canonical Transformations : A Comment on a “ A Lagrangian for DSR particle and the role of noncommutativity ”

The aim of this comment is to call to the attention of DSR readers a basic fact. The introduction of noncommutative structures in problems like the one addressed in [1] is not necessary for the understanding of DSR physics. It can be described just as the relativistic free particle problem in a different parametrization. An important task of mathematical physics is to prove that a given mathematical description of a physical theory is under some mild conditions " unique ". This is a difficult problem that can be tackled in principle with tools like consistent deformation, Lie algebra stability analysis and cohomology. A fundamental requirement for a good description of a physical theory is its invariance under field redefinitions. For example, one of the basic aims of the variational formulation in classical mechanics is precisely its covariance in configuration space.