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Cover: 9783319773704 | The Quantization of Gravity | Claus Gerhardt | Buch | Englisch | 2018
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The Quantization of Gravity
Buch von Claus Gerhardt
Sprache: Englisch

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Beschreibung
¿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.
¿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.
Über den Autor
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.
Zusammenfassung

Presents the first compelling model for quantum gravity

Offers a concise and comprehensive treatise

Can be understood with a graduate level knowledge of mathematics

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2018
Fachbereich: Theoretische Physik
Genre: Physik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 212
Reihe: Fundamental Theories of Physics
Inhalt: xii
200 S.
ISBN-13: 9783319773704
ISBN-10: 3319773704
Sprache: Englisch
Herstellernummer: 978-3-319-77370-4
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Gerhardt, Claus
Auflage: 1st ed. 2018
Hersteller: Springer International Publishing
Springer International Publishing AG
Fundamental Theories of Physics
Maße: 241 x 160 x 18 mm
Von/Mit: Claus Gerhardt
Erscheinungsdatum: 18.04.2018
Gewicht: 0,489 kg
preigu-id: 111302090
Über den Autor
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.
Zusammenfassung

Presents the first compelling model for quantum gravity

Offers a concise and comprehensive treatise

Can be understood with a graduate level knowledge of mathematics

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2018
Fachbereich: Theoretische Physik
Genre: Physik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 212
Reihe: Fundamental Theories of Physics
Inhalt: xii
200 S.
ISBN-13: 9783319773704
ISBN-10: 3319773704
Sprache: Englisch
Herstellernummer: 978-3-319-77370-4
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Gerhardt, Claus
Auflage: 1st ed. 2018
Hersteller: Springer International Publishing
Springer International Publishing AG
Fundamental Theories of Physics
Maße: 241 x 160 x 18 mm
Von/Mit: Claus Gerhardt
Erscheinungsdatum: 18.04.2018
Gewicht: 0,489 kg
preigu-id: 111302090
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