  We analyze the algebra of Dirac observables of the relativistic particle in
four space-time dimensions. We show that the position observables become
non-commutative and the commutation relations lead to a structure very similar
to the non-commutative geometry of Deformed Special Relativity (DSR). In this
framework, it appears natural to consider the 4d relativistic particle as a
five dimensional massless particle. We study its quantization in terms of wave
functions on the 5d light cone. We introduce the corresponding five-dimensional
action principle and analyze how it reproduces the physics of the 4d
relativistic particle. The formalism is naturally subject to divergences and we
show that DSR arises as a natural regularization: the 5d light cone is
regularized as the de Sitter space. We interpret the fifth coordinate as the
particle's proper time while the fifth moment can be understood as the mass.
Finally, we show how to formulate the Feynman propagator and the Feynman
amplitudes of quantum field theory in this context in terms of Dirac
observables. This provides new insights for the construction of observables and
scattering amplitudes in DSR.
