Chapter

Quantum geometrodynamics

Claus Kiefer

in Quantum Gravity

Published in print April 2012 | ISBN: 9780199585205
Published online May 2012 | e-ISBN: 9780191739378 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199585205.003.0005

Series: International Series of Monographs on Physics

Quantum geometrodynamics

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This chapter presents the quantization of canonical gravity in the metric formulation. The central equations are the Wheeler-DeWitt equation and the quantum diffeomorphism constraints, whose general properties are discussed at length. Special attention is focused on conceptual problems such as the problems of time and the inner product. The chapter includes general remarks on the functional Schr\"odinger picture, the connection with path integrals, and the extension of the formalism to quantum supergravity. A detailed section is devoted to the semiclassical approximation. Starting from quantum mechanical analogies, an approximate functional Schr\"odinger equation as well as quantum gravitational corrections are derived and discussed. Possible observational tests are pointed out.

Keywords: Quantum geometrodynamics; Wheeler-DeWitt equation; diffeomorphism constraints; problem of time; inner product; functional Schr\"odinger picture; supergravity; semiclassical approximation; observations

Chapter.  24855 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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