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Fundamental Theories of Physics

The Quantization of Gravity

Authors: Gerhardt, Claus

  • 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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eBook 83,29 €
price for Spain (gross)
  • ISBN 978-3-319-77371-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 103,99 €
price for Spain (gross)
  • ISBN 978-3-319-77370-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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 electro-magnetism, 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 self-adjoint 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

    Gerhardt, Claus

    Pages 1-50

    Preview Buy Chapter 30,19 €
  • Interaction of Gravity with Yang-Mills and Higgs Fields

    Gerhardt, Claus

    Pages 51-78

    Preview Buy Chapter 30,19 €
  • The Quantum Development of an Asymptotically Euclidean Cauchy Hypersurface

    Gerhardt, Claus

    Pages 79-97

    Preview Buy Chapter 30,19 €
  • The Quantization of a Schwarzschild-AdS Black Hole

    Gerhardt, Claus

    Pages 99-111

    Preview Buy Chapter 30,19 €
  • The Quantization of a Kerr-AdS Black Hole

    Gerhardt, Claus

    Pages 113-131

    Preview Buy Chapter 30,19 €

Buy this book

eBook 83,29 €
price for Spain (gross)
  • ISBN 978-3-319-77371-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 103,99 €
price for Spain (gross)
  • ISBN 978-3-319-77370-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
The Quantization of Gravity
Authors
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
978-3-319-77371-1
DOI
10.1007/978-3-319-77371-1
Hardcover ISBN
978-3-319-77370-4
Series ISSN
0168-1222
Edition Number
1
Number of Pages
XII, 200
Topics