Quantum gravitational corrections to the functional Schrödinger equation

Claus Kiefer and Tejinder P. Singh
Phys. Rev. D 44, 1067 – Published 15 August 1991
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Abstract

We derive corrections to the Schrödinger equation which arise from the quantization of the gravitational field. This is achieved through an expansion of the full functional Wheeler-DeWitt equation with respect to powers of the gravitational constant. The correction terms fall into two classes: One describes the breakdown of the classical background picture while the other corresponds to quantum gravitational corrections for the matter fields themselves. The latter are independent of the factor ordering which is chosen for the gravitational kinetic term. If the total state evolves adiabatically, the only correction term that survives contains the square of the matter Hamiltonian. In the general case there are also smaller terms which describe a gravitationally induced violation of unitarity. The corrections are numerically extremely tiny except near the big bang and the final stages of a black hole. They are also of principle significance for quantum field theories near the Planck scale.

  • Received 2 April 1991

DOI:https://doi.org/10.1103/PhysRevD.44.1067

©1991 American Physical Society

Authors & Affiliations

Claus Kiefer

  • Institut für Theoretische Physik der Universität Zürich, Schönberggasse 9, CH-8001 Zürich, Switzerland

Tejinder P. Singh

  • Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India and International Centre for Theoretical Physics, Trieste, Italy

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Issue

Vol. 44, Iss. 4 — 15 August 1991

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