The Quantization of Gravity

Nonfiction, Science & Nature, Science, Physics, Gravity, Cosmology
Cover of the book The Quantization of Gravity by Claus Gerhardt, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Claus Gerhardt ISBN: 9783319773711
Publisher: Springer International Publishing Publication: April 14, 2018
Imprint: Springer Language: English
Author: Claus Gerhardt
ISBN: 9783319773711
Publisher: Springer International Publishing
Publication: April 14, 2018
Imprint: Springer
Language: English

​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.  

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

​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.  

More books from Springer International Publishing

Cover of the book Sovereignty Referendums in International and Constitutional Law by Claus Gerhardt
Cover of the book Mind in Action by Claus Gerhardt
Cover of the book Applications and Usability of Interactive TV by Claus Gerhardt
Cover of the book Combinatorial Algorithms by Claus Gerhardt
Cover of the book From Chemistry to Consciousness by Claus Gerhardt
Cover of the book The Energy-Climate Continuum by Claus Gerhardt
Cover of the book The Modes of Human Rights Literature by Claus Gerhardt
Cover of the book Electromagnetic Brain Imaging by Claus Gerhardt
Cover of the book Hypergraph Theory by Claus Gerhardt
Cover of the book Brownian Motion and its Applications to Mathematical Analysis by Claus Gerhardt
Cover of the book Characterization of Metals and Alloys by Claus Gerhardt
Cover of the book Biotechnology and Production of Anti-Cancer Compounds by Claus Gerhardt
Cover of the book The Life, Science and Times of Lev Vasilevich Shubnikov by Claus Gerhardt
Cover of the book Photodynamic Therapy in Veterinary Medicine: From Basics to Clinical Practice by Claus Gerhardt
Cover of the book MVT: A Most Valuable Theorem by Claus Gerhardt
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy