Quantum mechanics of the gravitational field in asymptotically flat space

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Abstract
An expression for the propagation amplitude between two gravitational field configurations in asymptotically flat space is given. It depends on two three-geometries and on an element of the Poincaré group which specifies the relative location of two hyperplanes in the Minkowski space at infinity. The amplitude is obtained by path integrating over gravitational fields in the proper-time gauge which was previously used by the author for compact spaces. The causality condition, which is imposed by admitting in the path integral only positive proper-time separations between the initial and final surfaces, implies that the amplitude is not annihilated by the generator of normal deformations. It is argued that, as a consequence, it is not permissible to regard quantized gravitation theory in asymptotically flat space as an "ordinary gauge theory" even if one is only interested in asymptotic processes.

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