Quantization Gravity by Gerhardt Claus (37 results)
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Published by Springer, 2018
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Taschenbuch. Condition: Neu. The Quantization of Gravity | Claus Gerhardt | Taschenbuch | Fundamental Theories of Physics | xii | Englisch | 2018 | Springer | EAN 9783030084417 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: prei…gu.
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Taschenbuch. Condition: Neu. The Quantization of Gravity | Claus Gerhardt | Taschenbuch | Fundamental Theories of Physics | xii | Englisch | 2025 | Humana | EAN 9783031679247 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu….
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Published by Springer, 2018
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 findcorresponding eigendistributionsfor 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 areproducts 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.
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Published by Springer Verlag, 2018
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Paperback. Condition: Brand New. reprint edition. 216 pages. 9.25x6.10x0.49 inches. In Stock.
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Published by Springer, 2024
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Published by Springer Nature Switzerland, Springer International Publishing, 2024
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 hyperbolic equation in a fiber bundle, where the base space represents a Cauchy hypersurface of the quantized spacetime and the fibers the Riemannian metrics in the base space. The hyperbolic operator, a second order partial differential operator, acts both in the fibers as well as in the base space. In this second edition new results are presentedwhich allow the solutions of the hyperbolic equation to be expressedas products of spatial and temporal eigenfunctions of self-adjoint operators. These eigenfunctions form complete bases in appropriate Hilbert spaces. The eigenfunctions depending on the fiber elements are a subset of the Fourier kernel of the symmetric space SL(n,R)/SO(n), where n is the dimension of the base space; they represent the elementary gravitons corresponding to the degrees of freedom in choosing the entries of Riemannian metrics with determinants equal to one. These are all the degrees of freedom available because of the coordinate system invariance: For any smooth Riemannian metric there exists an atlas such that in each chart the determinant of the metric is equal to one. In the important case n=3 the Standard Model could also be incorporated such that one can speak of a unified quantization of all four fundamental forces of nature.
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Published by Springer Nature, 2024
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Published by Springer International Publishing Dez 2018, 2018
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware - 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 findcorresponding eigendistributionsfor 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 areproducts 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. 216 pp. Englisch.
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 hyperbolic equation in a fiber bundle, where the base space represents a Cauchy hypersurface of the quantized spacetime and the fibers the Riemannian metrics in the base space. The hyperbolic operator, a second order partial differential operator, acts both in the fibers as well as in the base space. In this second edition new results are presentedwhich allow the solutions of the hyperbolic equation to be expressedas products of spatial and temporal eigenfunctions of self-adjoint operators. These eigenfunctions form complete bases in appropriate Hilbert spaces. The eigenfunctions depending on the fiber elements are a subset of the Fourier kernel of the symmetric space SL(n,R)/SO(n), where n is the dimension of the base space; they represent the elementary gravitons corresponding to the degrees of freedom in choosing the entries of Riemannian metrics with determinants equal to one. These are all the degrees of freedom available because of the coordinate system invariance: For any smooth Riemannian metric there exists an atlas such that in each chart the determinant of the metric is equal to one. In the important case n=3 the Standard Model could also be incorporated such that one can speak of a unified quantization of all four fundamental forces of nature. 264 pp. Englisch.
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 quantiz…ation 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 hyperbolic equation in a fiber bundle, where the base space represents a Cauchy hypersurface of the quantized spacetime and the fibers the Riemannian metrics in the base space. The hyperbolic operator, a second order partial differential operator, acts both in the fibers as well as in the base space. In this second edition new results are presentedwhich allow the solutions of the hyperbolic equation to be expressedas products of spatial and temporal eigenfunctions of self-adjoint operators. These eigenfunctions form complete bases in appropriate Hilbert spaces. The eigenfunctions depending on the fiber elements are a subset of the Fourier kernel of the symmetric space SL(n,R)/SO(n), where n is the dimension of the base space; they represent the elementary gravitons corresponding to the degrees of freedom in choosing the entries of Riemannian metrics with determinants equal to one. These are all the degrees of freedom available because of the coordinate system invariance: For any smooth Riemannian metric there exists an atlas such that in each chart the determinant of the metric is equal to one. In the important case n=3 the Standard Model could also be incorporated such that one can speak of a unified quantization of all four fundamental forces of nature. 264 pp. Englisch.
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