  We show the existence of a noncommutative spacetime structure in the context
of a complete discussion on the underlying spacetime symmetries for the
physical system of a free massless relativistic particle. The above spacetime
symmetry transformations are discussed for the first-order Lagrangian of the
system where the transformations on the coordinates, velocities and momenta
play very important roles. We discuss the dynamics of this system in a
systematic manner by exploiting the symplectic structures associated with the
four dimensional (non-)commutative cotangent (i.e. momentum phase) space
corresponding to a two dimensional (non-)commutative configuration (i.e.
target) space. A simple connection of the above noncommutativity (NC) is
established with the NC associated with the subject of quantum groups where
$SL_{q,q^{-1}} (2)$ transformations play a decisive role.
