The Quantization Of Gravity

Author : Claus Gerhardt
Publisher : Springer
ISBN 13 : 3319773712
Total Pages : 200 pages
Book Rating : 4.11/5 ( download)

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Download or read book The Quantization of Gravity written by Claus Gerhardt and published by Springer. This book was released on 2018-04-14 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​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.

Author : Claus Gerhardt
Publisher : Springer
ISBN 13 : 9783031679216
Total Pages : 0 pages
Book Rating : 4.10/5 ( download)

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Download or read book The Quantization of Gravity written by Claus Gerhardt and published by Springer. This book was released on 2024-10-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 presented which allow the solutions of the hyperbolic equation to be expressed as 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.

Author : Sabine Hossenfelder
Publisher : Springer
ISBN 13 : 3319645374
Total Pages : 120 pages
Book Rating : 4.77/5 ( download)

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Download or read book Experimental Search for Quantum Gravity written by Sabine Hossenfelder and published by Springer. This book was released on 2017-11-15 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes recent developments in the research area of quantum gravity phenomenology. A series of short and nontechnical essays lays out the prospects of various experimental possibilities and their current status. Finding observational evidence for the quantization of space-time was long thought impossible. In the last decade however, new experimental design and technological advances have changed the research landscape and opened new perspectives on quantum gravity. Formerly dominated by purely theoretical constructions, quantum gravity now has a lively phenomenology to offer. From high precision measurements using macroscopic quantum oscillators to new analysis methods of the cosmic microwave background, no stone is being left unturned in the experimental search for quantum gravity. This book sheds new light on the connection of astroparticle physics with the quantum gravity problem. Gravitational waves and their detection are covered. It illustrates findings from the interconnection between general relativity, black holes and Planck stars. Finally, the return on investment in quantum-gravitation research is illuminated. The book is intended for graduate students and researchers entering the field.

Author : Steven Carlip
Publisher : Cambridge University Press
ISBN 13 : 9780521545884
Total Pages : 296 pages
Book Rating : 4.89/5 ( download)

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Download or read book Quantum Gravity in 2+1 Dimensions written by Steven Carlip and published by Cambridge University Press. This book was released on 2003-12-04 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive survey of (2+1)-dimensional quantum gravity - for graduate students and researchers.

Author : Lee Smolin
Publisher : Basic Books
ISBN 13 : 0465013244
Total Pages : 230 pages
Book Rating : 4.41/5 ( download)

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Download or read book Three Roads To Quantum Gravity written by Lee Smolin and published by Basic Books. This book was released on 2008-03-18 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: "It would be hard to imagine a better guide to this difficult subject." -- Scientific American In Three Roads to Quantum Gravity, Lee Smolin provides an accessible overview of the attempts to build a final "theory of everything." He explains in simple terms what scientists are talking about when they say the world is made from exotic entities such as loops, strings, and black holes and tells the fascinating stories behind these discoveries: the rivalries, epiphanies, and intrigues he witnessed firsthand. "Provocative, original, and unsettling." -- The New York Review of Books "An excellent writer, a creative thinker." -- Nature

Author : Claus Kiefer
Publisher : Oxford University Press
ISBN 13 : 0199585202
Total Pages : 406 pages
Book Rating : 4.05/5 ( download)

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Download or read book Quantum Gravity written by Claus Kiefer and published by Oxford University Press. This book was released on 2012-04-05 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum theory and Einstein's theory of relativity are at the centre of modern theoretical physics, yet, the consistent unification of both theories is still elusive. This book offers an up-to-date introduction into the attempts to construct a unified theory of "quantum gravity".

Author : Horst-Heino Borzeszkowski
Publisher : Springer
ISBN 13 : 9789401082297
Total Pages : 132 pages
Book Rating : 4.94/5 ( download)

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Download or read book The Meaning of Quantum Gravity written by Horst-Heino Borzeszkowski and published by Springer. This book was released on 2011-09-26 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: In discussing the question of whether General Relativity Theory really needs to be quantized, a simply negative answer cannot be accepted, of course. Such an answer is not satisfying because, first, Einstein's gravitational equations connect gravity and non-gravitational matter and because, second, it can be taken for granted that non-gravitational matter has an atomic or quantum structure such that its energy-momentum tensor standing on the right-hand side of Einstein's equations is formed out of quantum operators. These two facts make it impossible to read the left-hand side of Einstein's equations as an ordinary classical function. This does not necessarily mean, however, that we must draw the conclusion that General Relativity Theory, similar to electrodynamics, could or should be quantized in a rigorous manner and that this quantization has similar consequences to quantum electrodynamics. In other words, when for reasons of consistency quantization is tried, then one has to ask whether and where the quantization procedure has a physical meaning, i.e., whether there exist measurable effects of quantum gravity. IQ accordance with these questions, we are mainly dealing with the discus sion of the principles of quantized General Relativity Theory and with the estimation of quantum effects including the question of their measurability. This analysis proves that it is impossible to distinguish between classical and quantum General Relativity Theory for the extreme case of Planck's orders of magnitude. In other words, there does not exist a physically meaningful rigorous quantization conception for Einstein's theory.

Author : Herbert W. Hamber
Publisher : Springer Science & Business Media
ISBN 13 : 354085293X
Total Pages : 342 pages
Book Rating : 4.33/5 ( download)

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Download or read book Quantum Gravitation written by Herbert W. Hamber and published by Springer Science & Business Media. This book was released on 2008-10-20 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Quantum Gravitation" approaches the subject from the point of view of Feynman path integrals, which provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. It is shown that the path integral method is suitable for both perturbative as well as non-perturbative studies, and is already known to offer a framework for the theoretical investigation of non-Abelian gauge theories, the basis for three of the four known fundamental forces in nature. The book thus provides a coherent outline of the present status of the theory gravity based on Feynman’s formulation, with an emphasis on quantitative results. Topics are organized in such a way that the correspondence to similar methods and results in modern gauge theories becomes apparent. Covariant perturbation theory are developed using the full machinery of Feynman rules, gauge fixing, background methods and ghosts. The renormalization group for gravity and the existence of non-trivial ultraviolet fixed points are investigated, stressing a close correspondence with well understood statistical field theory models. The final chapter addresses contemporary issues in quantum cosmology such as scale dependent gravitational constants and quantum effects in the early universe.

Author : Viatcheslav Mukhanov
Publisher : Cambridge University Press
ISBN 13 : 9780521868341
Total Pages : 298 pages
Book Rating : 4.43/5 ( download)

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Download or read book Introduction to Quantum Effects in Gravity written by Viatcheslav Mukhanov and published by Cambridge University Press. This book was released on 2007-06-14 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher description

Author : Rodolfo Gambini
Publisher : OUP Oxford
ISBN 13 : 0191003239
Total Pages : 192 pages
Book Rating : 4.33/5 ( download)

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Download or read book A First Course in Loop Quantum Gravity written by Rodolfo Gambini and published by OUP Oxford. This book was released on 2011-09-22 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to loop quantum gravity and some of its applications, at a level suitable for undergraduate students and others with only a minimal knowledge of college level physics. In particular it is not assumed that the reader is familiar with general relativity and only minimally familiar with quantum mechanics and Hamiltonian mechanics. Most chapters end with problems that elaborate on the text, and aid learning. Applications such as loop quantum cosmology, black hole entropy and spin foams are briefly covered. The text is ideally suited for an undergraduate course in the senior year of a physics major. It can also be used to introduce undergraduates to general relativity and quantum field theory as part of a 'special topics' type of course.