  In the presence of a cosmological constant, interpreted as a purely geometric
entity, absence of matter is represented by a de Sitter spacetime. As a
consequence, ordinary Poincare' special relativity is no longer valid and must
be replaced by a de Sitter special relativity. By considering the kinematics of
a spinless particle in a de Sitter spacetime, we study the geodesics of this
spacetime, the ensuing definitions of canonical momenta, and explore possible
implications for quantum mechanics.
