Otto C. W. Kong, Jason Payne (Nat'l Central Univ., Taiwan)
In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics in it intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting point of the formulation is the representations of the relativity symmetries. Moreover, that seriously furnishes -- via the notion of symmetry contractions -- a natural way in which one can understand how the Newtonian theory arise as an approximation to Einstein's theory. We begin with the Poincaré symmetry underlying special relativity and the nature of Minkowski spacetime as a coset representation space of the algebra and the group, as well as how the representation. Then, we proceed to the parallel for the phase space of a particle, in relation to which we present the full scheme for its dynamics under the Hamiltonian formulation illustrating that as essentially the symmetry feature of the phase space geometry. Lastly, the reduction of all that to the Newtonian theory as an approximation with its space-time, phase space, and dynamics under the appropriate relativity symmetry contraction is presented.
