A new look at the Ashtekar-Magnon energy condition

Abstract

Quantum field theory has enjoyed much success, indeed for ordinary flat spacetime applications it has been experimentally verified to a great deal of accuracy. However on general cursed spacetime backgrounds there is no canonical method for constructing a quantum field theory. In 1975, Abhay Ashtekar and Anne Magnon made progress toward the goal of obtaining a canonical quantization procedure for scalar fields on a curved spacetime background. By considering spacetimes on which a quantum theory had been well established, they identified a physical condition (the energy condition) that the scalar fields satisfy. They proved that this energy condition selects a unique quantization procedure for certain observers in general, curved spacetimes. Here we state and prove a stronger and more general result and discuss applications of this result. The first application recovers the result of Ashtekar and Magnon as a special case, while the second application is concerned with the more general case when the scalar field is coupled to the scalar curvature of the underlying spacetime.