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The Quantization of Gravity

  • Couverture cartonnée
  • 216 Nombre de pages
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A unified quantum theory incorporating the four fundamental forces of nature is one of the major open problems in physics. The Sta... Lire la suite
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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.

Presents the first compelling model for quantum gravity

Offers a concise and comprehensive treatise

Can be understood with a graduate level knowledge of mathematics

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.


Informations sur le produit

Titre: The Quantization of Gravity
Code EAN: 9783030084417
ISBN: 3030084418
Format: Couverture cartonnée
Editeur: Springer International Publishing
nombre de pages: 216
Poids: 335g
Taille: H235mm x B155mm x T11mm
Année: 2018
Auflage: Softcover reprint of the original 1st ed. 2018