Abstract
It is verified explicitly to second order in Newton's constant, , that the quantum-tree-graph contribution to the vacuum expectation value of the gravitational field produced by a spherically symmetric -number source correctly reproduces the classical Schwarzschild solution. If the source is taken to be that of a point mass, then even the tree diagrams are divergent, and it is necessary to use a source of finite extension which, for convenience, is taken to be a perfect fluid sphere with uniform density. In this way both the interior and exterior solutions may be generated. A mass renormalization takes place; the total mass of the source, , being related to its bare mass, , and invariant radius, , by the Newtonian-like formula, , and the infinities in the quantum theory are seen to be a manifestation of the divergent self-energy problem encountered in classical mechanics.
- Received 7 July 1972
DOI:https://doi.org/10.1103/PhysRevD.7.2317
©1973 American Physical Society