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Phys. Rev. 177, 1929–1941 (1969)

Derivation of the Ten Einstein Field Equations from the Semiclassical Approximation to Quantum Geometrodynamics

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Ulrich H. Gerlach*
Palmer Physical Laboratory, Princeton University, Princeton, New Jersey 08540
Battelle Memorial Institute, Columbus, Ohio 43201

Received 20 September 1968; published in the issue dated January 1969

All ten Einstein field equations are derived from (a) a single equation, the Einstein-Hamilton-Jacobi equation for general relativity, and (b) the principle of constructive interference of de Broglie waves in superspace. In this derivation one obtains by introducing Tomonaga's many-time parametrization the manifestly covariant Hamiltonian equations of general relativity.

© 1969 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRev.177.1929
DOI:
10.1103/PhysRev.177.1929
PACS:

*Present address: Battelle Memorial Institute, Columbus, Ohio.