1969•Physical ReviewRequires access

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

Ulrich H. Gerlach

Abstract

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.

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Key concepts: Physics, Introduction to the mathematics of general relativity, Semiclassical physics, Mathematical physics, General relativity, Einstein field equations, Covariant transformation, Classical field theory