The Quantization of Gravity
Springer International Publishing (Verlag)
978-3-030-08441-7 (ISBN)
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.
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.
The quantization of a globally hyperbolic spacetime.- Interaction of gravity with Yang-Mills and Higgs fields.- The quantum development of an asymptotically Euclidean Cauchy hypersurface.- The quantization of a Schwarzschild-AdS black hole.- The quantization of a Kerr-AdS black hole.- A partition function for quantized globally hyperbolic spacetimes with a negative cosmological constant.- Appendix.
"This is an interesting as well as an important book. ... The book is, of course, well written, elegant, and well balanced. ... for anyone doing research in quantizing gravity, the procedure and framework offered by this book will provide a wider and more complete perspective on the challenge. In other words, this should become a textbook or a cited reference for consultation in any advanced course where quantum gravity is one of the main topics." (Paulo Moniz, Mathematical Reviews, July, 2019)
“This is an interesting as well as an important book. … The book is, of course, well written, elegant, and well balanced. … for anyone doing research in quantizing gravity, the procedure and framework offered by this book will provide a wider and more complete perspective on the challenge. In other words, this should become a textbook or a cited reference for consultation in any advanced course where quantum gravity is one of the main topics.” (Paulo Moniz, Mathematical Reviews, July, 2019)
| Erscheinungsdatum | 05.03.2022 |
|---|---|
| Reihe/Serie | Fundamental Theories of Physics |
| Zusatzinfo | XII, 200 p. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 338 g |
| Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik |
| Schlagworte | Dark energy density • Explaining dark matter and dark energy • Mass gap • Quantization of gravity • Quantum Statistics • Quantum theory of gravity • Spinor field • Unified Field Theory • Unified quantum theory • Yang-Mills field |
| ISBN-10 | 3-030-08441-8 / 3030084418 |
| ISBN-13 | 978-3-030-08441-7 / 9783030084417 |
| Zustand | Neuware |
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