Duality of Coordinates and Matter Fields in Curved Spacetime

Abstract

We show that there exists a duality between the local coordinates and the solutions of the Klein-Gordon equation in curved spacetime in the same sense as in the Minkowski spacetime. However, the duality in curved spacetime does not have the same generality as in flat spacetime and it holds only if the system satisfies certain constraints. We derive these constraints and the basic equations of duality and discuss the implications in the quantum theory.

14 pages, ReVTeX file. Comments added, to appear in Phys.Lett.B

References in corpus (1)

• The quantum structure of spacetime at the Planck scale and quantum fields

Cited by in corpus (3)

• Equivalence Principle, Higher Dimensional Moebius Group and the Hidden Antisymmetric Tensor of Quantum Mechanics
• Duality between coordinates and Dirac field
• Duality between the coordinates and wave functions on noncommutative space