 Presents the first compelling model for quantum gravity
 Offers a concise and comprehensive treatise
 Can be understood with a graduate level knowledge of mathematics
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 About this book

A unified quantum theory incorporating the four fundamental forces of nature is one of the major open problems in physics. The Standard Model combines electromagnetism, the strong force and the weak force, but ignores gravity. The quantization of gravity is therefore a necessary first step to achieve a unified quantum theory. In this monograph a canonical quantization of gravity has been achieved by quantizing a geometric evolution equation resulting in a gravitational wave equation in a globally hyperbolic spacetime. Applying the technique of separation of variables we obtain eigenvalue problems for temporal and spatial selfadjoint operators where the temporal operator has a pure point spectrum with eigenvalues $\lambda_i$ and related eigenfunctions, while, for the spatial operator, it is possible to find corresponding eigendistributions for each of the eigenvalues $\lambda_i$, if the Cauchy hypersurface is asymptotically Euclidean or if the quantized spacetime is a black hole with a negative cosmological constant. The hyperbolic equation then has a sequence of smooth solutions which are products of temporal eigenfunctions and spatial eigendistributions. Due to this "spectral resolution" of the wave equation quantum statistics can also be applied to the quantized systems. These quantum statistical results could help to explain the nature of dark matter and dark energy.
 About the authors

Claus Gerhardt is a professor of mathematics at the University of Heidelberg. His research areas are partial differential equations, differential geometry and general relativity. He is especially interested in geometric evolution equations in Riemannian or Lorentzian manifolds and in applying these geometric ideas and techniques to open problems in mathematics and physics.
 Table of contents (8 chapters)


The Quantization of a Globally Hyperbolic Spacetime
Pages 150

Interaction of Gravity with YangMills and Higgs Fields
Pages 5178

The Quantum Development of an Asymptotically Euclidean Cauchy Hypersurface
Pages 7997

The Quantization of a SchwarzschildAdS Black Hole
Pages 99111

The Quantization of a KerrAdS Black Hole
Pages 113131

Table of contents (8 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 The Quantization of Gravity
 Authors

 Claus Gerhardt
 Series Title
 Fundamental Theories of Physics
 Series Volume
 194
 Copyright
 2018
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer International Publishing AG, part of Springer Nature
 eBook ISBN
 9783319773711
 DOI
 10.1007/9783319773711
 Hardcover ISBN
 9783319773704
 Series ISSN
 01681222
 Edition Number
 1
 Number of Pages
 XII, 200
 Topics