Duality of coordinates and matter fields in curved spacetime

We show that there exists a duality between the local coordinates and the s olutions of the Klein-Gerdon equation in curved spacetime in the same sense as in the Minkowski spacetime. However, the duality in curved spacetime do es not have the same generality as in flat spacetime and it holds only if t he system satisfies certain constraints. We derive these constraints and th e basic equations of duality and discuss the implications in the quantum th eory. (C) 2000 Elsevier Science B.V. All rights reserved.